rcv helps you work directly with raw ballot image and cast vote record
data to tabulate and visualize ranked choice election results.
Features
- Read in ballot image and master lookup files
- Merge these files to get a “readable” ballot layout
- Conduct elections, and view a round-by-round table of results
- Visualize the flow of voters with an interactive Sankey diagram
Installation
We’re on CRAN now! You can install our latest release (0.2.2):
install.packages("rcv")Or, you can install the development version of rcv here:
devtools::install_github("jayleetx/rcv")This package grew out a class project for Math 241 at Reed College, taught by Dr. Andrew Bray. Matthew Yancheff and Mia Leung were instrumental in earlier phases of this package and project.
The style of this README is inspired by the googlesheets R package.
sf_bos_ballot is included as an example raw ballot image, and
sf_bos_lookup as an example raw master lookup. Both are included as
.rdas, and they are in the “WinEDS” format. This data comes from the
2016 San Francisco Board of Supervisors elections (San Francisco
Department of
Elections).
head(sf_bos_ballot)## # A tibble: 6 x 1
## X1
## <chr>
## 1 000000900000660300000010020000406001000012800
## 2 000000900000660300000010020000406002000000001
## 3 000000900000660300000010020000406003000000001
## 4 000000900000660400000010020000406001000012300
## 5 000000900000660400000010020000406002000012500
## 6 000000900000660400000010020000406003000012100
head(sf_bos_lookup)## # A tibble: 6 x 1
## X1
## <chr>
## 1 Candidate 0000121SAMUEL KWONG 0000001000~
## 2 Candidate 0000131TIM E. DONNELLY 0000001000~
## 3 Candidate 0000133DEAN PRESTON 0000001000~
## 4 Candidate 0000135JOEL ENGARDIO 0000001000~
## 5 Candidate 0000140MELISSA SAN MIGUEL 0000001000~
## 6 Candidate 0000144AHSHA SAFAI 0000001000~
The streamlined version of this process is done with the
clean_ballot() function. b_header and l_header are logical values,
based on whether the ballot and lookup file respectively have a header
for the first row.
cleaned <- clean_ballot(ballot = sf_bos_ballot,
lookup = sf_bos_lookup,
format = "WinEDS")
knitr::kable(head(readable(cleaned)))| contest | pref_voter_id | 1 | 2 | 3 |
|---|---|---|---|---|
| Board of Supervisors, District 1 | 000006603 | SANDRA LEE FEWER | NA | NA |
| Board of Supervisors, District 1 | 000006604 | MARJAN PHILHOUR | DAVID LEE | SAMUEL KWONG |
| Board of Supervisors, District 1 | 000006605 | DAVID LEE | RICHIE GREENBERG | BRIAN J. LARKIN |
| Board of Supervisors, District 1 | 000006606 | MARJAN PHILHOUR | DAVID LEE | SANDRA LEE FEWER |
| Board of Supervisors, District 1 | 000006607 | BRIAN J. LARKIN | ANDY THORNLEY | JASON JUNGREIS |
| Board of Supervisors, District 1 | 000006608 | MARJAN PHILHOUR | NA | NA |
To access intermediate steps, the following process can be used.
# Import and label ballot image
a <- sf_bos_ballot %>%
label(image = "ballot", format = "WinEDS")
# Import and label master lookup
b <- sf_bos_lookup %>%
label(image = "lookup", format = "WinEDS")
# Merge these two tables
c <- characterize(ballot = a, lookup = b, format = "WinEDS")
knitr::kable(head(readable(c)))| contest | pref_voter_id | 1 | 2 | 3 |
|---|---|---|---|---|
| Board of Supervisors, District 1 | 000006603 | SANDRA LEE FEWER | NA | NA |
| Board of Supervisors, District 1 | 000006604 | MARJAN PHILHOUR | DAVID LEE | SAMUEL KWONG |
| Board of Supervisors, District 1 | 000006605 | DAVID LEE | RICHIE GREENBERG | BRIAN J. LARKIN |
| Board of Supervisors, District 1 | 000006606 | MARJAN PHILHOUR | DAVID LEE | SANDRA LEE FEWER |
| Board of Supervisors, District 1 | 000006607 | BRIAN J. LARKIN | ANDY THORNLEY | JASON JUNGREIS |
| Board of Supervisors, District 1 | 000006608 | MARJAN PHILHOUR | NA | NA |
The readable() function takes the clean image, which is formatted for
ease in computation, and formats it to be easily read manually.
This is done with the rcv_tally() function. sf_bos_clean is included
as an example of a pre-cleaned ballot using the functions above. We will
run the District 1 election from this ballot image.
results <- rcv_tally(sf_bos_clean, "Board of Supervisors, District 1")
knitr::kable(results)| candidate | round1 | round2 | round3 | round4 | round5 | round6 | round7 | round8 | round9 | round10 | round11 | round12 | round13 | round14 | round15 | round16 | round17 | round18 | round19 | round20 | round21 | round22 | round23 | round24 | round25 | round26 | round27 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| LONDON BREED | 21318 | 21318 | 21318 | 21318 | 21318 | 21318 | 21318 | 21318 | 21318 | 21318 | 21318 | 21318 | 21318 | 21318 | 21318 | 21318 | 21318 | 21318 | 21318 | 21318 | 21318 | 21318 | 21318 | 30301 | 30301 | 30301 | 30301 |
| HILLARY RONEN | 18335 | 18335 | 18460 | 18460 | 18460 | 18460 | 18460 | 18460 | 18460 | 18460 | 18460 | 18460 | 20166 | 20166 | 20166 | 20166 | 20166 | 20166 | 20166 | 25696 | 25696 | 25696 | 25696 | 25696 | 25696 | 25696 | 25696 |
| AARON PESKIN | 19093 | 19093 | 19093 | 19093 | 19093 | 19093 | 19093 | 19093 | 19093 | 19093 | 19093 | 19093 | 19093 | 19093 | 19093 | 19093 | 22254 | 22254 | 22254 | 22254 | 22254 | 22254 | 22254 | 22254 | 22254 | 22254 | NA |
| SANDRA LEE FEWER | 12550 | 12689 | 12689 | 12777 | 12840 | 13029 | 13093 | 13225 | 13354 | 13354 | 13354 | 13354 | 13354 | 14705 | 14705 | 14705 | 14705 | 14705 | 14705 | 14705 | 14705 | 20074 | 20074 | 20074 | 20074 | NA | NA |
| NORMAN YEE | 14154 | 14154 | 14154 | 14154 | 14154 | 14154 | 14154 | 14154 | 14154 | 14154 | 14644 | 14644 | 14644 | 14644 | 14644 | 15630 | 15630 | 17184 | 17184 | 17184 | 20038 | 20038 | 20038 | 20038 | NA | NA | NA |
| DEAN PRESTON | 19534 | 19534 | 19534 | 19534 | 19534 | 19534 | 19534 | 19534 | 19534 | 19534 | 19534 | 19534 | 19534 | 19534 | 19534 | 19534 | 19534 | 19534 | 19534 | 19534 | 19534 | 19534 | 19534 | NA | NA | NA | NA |
| AHSHA SAFAI | 9422 | 9422 | 9422 | 9422 | 9422 | 9422 | 9422 | 9422 | 9422 | 9652 | 9652 | 10130 | 10130 | 10130 | 10895 | 10895 | 10895 | 10895 | 13984 | 13984 | 13984 | 13984 | NA | NA | NA | NA | NA |
| MARJAN PHILHOUR | 11067 | 11135 | 11135 | 11247 | 11348 | 11487 | 11680 | 11837 | 12086 | 12086 | 12086 | 12086 | 12086 | 13126 | 13126 | 13126 | 13126 | 13126 | 13126 | 13126 | 13126 | NA | NA | NA | NA | NA | NA |
| JOEL ENGARDIO | 7630 | 7630 | 7630 | 7630 | 7630 | 7630 | 7630 | 7630 | 7630 | 7630 | 7960 | 7960 | 7960 | 7960 | 7960 | 9360 | 9360 | 12050 | 12050 | 12050 | NA | NA | NA | NA | NA | NA | NA |
| JOSHUA ARCE | 9612 | 9612 | 9722 | 9722 | 9722 | 9722 | 9722 | 9722 | 9722 | 9722 | 9722 | 9722 | 10911 | 10911 | 10911 | 10911 | 10911 | 10911 | 10911 | NA | NA | NA | NA | NA | NA | NA | NA |
| KIM ALVARENGA | 8640 | 8640 | 8640 | 8640 | 8640 | 8640 | 8640 | 8640 | 8640 | 8931 | 8931 | 9633 | 9633 | 9633 | 10445 | 10445 | 10445 | 10445 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| BEN MATRANGA | 6475 | 6475 | 6475 | 6475 | 6475 | 6475 | 6475 | 6475 | 6475 | 6475 | 6809 | 6809 | 6809 | 6809 | 6809 | 8462 | 8462 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| TIM E. DONNELLY | 7395 | 7395 | 7395 | 7395 | 7395 | 7395 | 7395 | 7395 | 7395 | 7395 | 7395 | 7395 | 7395 | 7395 | 7395 | 7395 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| JOHN FARRELL | 4927 | 4927 | 4927 | 4927 | 4927 | 4927 | 4927 | 4927 | 4927 | 4927 | 5534 | 5534 | 5534 | 5534 | 5534 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| MAGDALENA DE GUZMAN | 3001 | 3001 | 3001 | 3001 | 3001 | 3001 | 3001 | 3001 | 3001 | 3477 | 3477 | 4450 | 4450 | 4450 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| DAVID LEE | 3396 | 3408 | 3408 | 3488 | 3551 | 3622 | 3857 | 3961 | 4093 | 4093 | 4093 | 4093 | 4093 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| MELISSA SAN MIGUEL | 3439 | 3439 | 3640 | 3640 | 3640 | 3640 | 3640 | 3640 | 3640 | 3640 | 3640 | 3640 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| FRANCISCO HERRERA | 2598 | 2598 | 2598 | 2598 | 2598 | 2598 | 2598 | 2598 | 2598 | 3037 | 3037 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| MIKE YOUNG | 1995 | 1995 | 1995 | 1995 | 1995 | 1995 | 1995 | 1995 | 1995 | 1995 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| BERTA HERNANDEZ | 1599 | 1599 | 1599 | 1599 | 1599 | 1599 | 1599 | 1599 | 1599 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| RICHIE GREENBERG | 974 | 984 | 984 | 1042 | 1220 | 1272 | 1386 | 1508 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| BRIAN J. LARKIN | 747 | 773 | 773 | 832 | 896 | 956 | 997 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| SAMUEL KWONG | 740 | 744 | 744 | 760 | 785 | 814 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| JONATHAN LYENS | 609 | 652 | 652 | 679 | 726 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| JASON JUNGREIS | 611 | 626 | 626 | 654 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| SHERMAN R. D’SILVA | 557 | 566 | 566 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| ISWARI ESPAÑA | 539 | 539 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| ANDY THORNLEY | 359 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| NA | 23286 | 23319 | 23422 | 23520 | 23633 | 23819 | 23986 | 24468 | 25466 | 25629 | 25863 | 26747 | 27492 | 29194 | 32067 | 33562 | 37796 | 42014 | 49370 | 54751 | 63947 | 71704 | 85688 | 96239 | 116277 | 136351 | 158605 |
Sandra Lee Fewer wins in Round 9, with 14,705 votes to Marjan Philhour’s 13,126. 3,499 ballots were left blank for this election, and 3,779 were exhausted or marked invalid in this election.
We have two recommended methods of visualizing RCV data. Both utilize a flowchart called a “Sankey diagram” to show the transfer of voters between rounds. We will use each method to visualize the transfer of voters in the San Francisco District 7 Board of Supervisors election, because District 1 has too many crossings to be readable.
Method 1 (preferred because it is interactive, quicker, and more
readable) uses the networkD3 package:
d3_7 <- rcv::make_d3list(results = sf_7_results)
networkD3::sankeyNetwork(Links = d3_7$values, Nodes = d3_7$names,
Source = "source", Target = "target",
Value = "value", NodeID = "candidate", units = "voters",
fontSize = 12, nodeWidth = 20)
Method 2 uses the alluvial package (this type of graphic is also
called an alluvial diagram):
alluvial_7 <- rcv::make_alluvialdf(image = sf_bos_clean,
rcvcontest = "Board of Supervisors, District 7")## Warning: `count_()` was deprecated in dplyr 0.7.0.
## Please use `count()` instead.
## See vignette('programming') for more help
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning in min(rank): no non-missing arguments to min; returning Inf
## Warning: `group_by_()` was deprecated in dplyr 0.7.0.
## Please use `group_by()` instead.
## See vignette('programming') for more help
alluvial::alluvial(
alluvial_7[,1:4], freq = alluvial_7$frequency,
col = ifelse(alluvial_7$round4 == "NORMAN YEE", "lightgreen", "gray"),
border = "gray", alpha = 0.7, blocks = TRUE
)