Ranked-ballot voting calculator

This form calculates the winners of several ranked-ballot voting methods.  See below for input examples.

Enter ranked ballots:

Enter candidates to ignore (optional):

Enter tiebreaking ranking (optional):

Reverse all rankings

Or see how a specific method chooses its winner:


Each line must consist of candidate names separated by > or =.  Each candidate name must be one word and consist only of uppercase and lowercase letters (case is significant, so LeGrand is not the same as Legrand).  One ballot per line is assumed unless the line begins with a number followed by a colon; the number specifies how many ballots share that ranking.  If a candidate appears more than once on a line, only the first (highest) occurrence is counted.  A # begins a comment that extends to the end of the line; the calculator ignores comments.  Ballots themselves can be commented out by inserting a # at the beginning of the line.

If a list of candidates to ignore is given, those candidates will be treated as if they dropped out of the election between the collection and counting of the ballots.

If a tiebreaking ranking is given, it must include all of the candidates.  If none is given and a tiebreaking ranking is needed, it will be generated by drawing a random ballot and breaking its tied preferences randomly.

Checking the “Reverse all rankings” box effectively flips the preferences in each ballot and in the tiebreaker; it’s useful to test for reverse-symmetry violations.

Here are some example ranked-ballot inputs to use.  Just copy one of these text blocks and paste it into the input field above.  See if you can guess the results!

# example from method description page
 98:Abby>Cora>Erin>Dave>Brad
 64:Brad>Abby>Erin>Cora>Dave
 12:Brad>Abby>Erin>Dave>Cora
 98:Brad>Erin>Abby>Cora>Dave
 13:Brad>Erin>Abby>Dave>Cora
125:Brad>Erin>Dave>Abby>Cora
124:Cora>Abby>Erin>Dave>Brad
 76:Cora>Erin>Abby>Dave>Brad
 21:Dave>Abby>Brad>Erin>Cora
 30:Dave>Brad>Abby>Erin>Cora
 98:Dave>Brad>Erin>Cora>Abby
139:Dave>Cora>Abby>Brad>Erin
 23:Dave>Cora>Brad>Abby>Erin

# 1980 American presidential election
45:Reagan>Anderson>Carter
20:Anderson>Carter>Reagan
35:Carter>Anderson>Reagan

# 1860 American presidential election
2117:Lincoln>Douglas>Bell>Breckinridge
1861:Lincoln>Bell>Douglas>Breckinridge
1119:Breckinridge>Bell>Douglas>Lincoln
 859:Douglas>Bell>Lincoln>Breckinridge
 804:Douglas>Lincoln>Bell>Breckinridge
 753:Douglas>Bell>Breckinridge>Lincoln
 687:Breckinridge>Douglas>Bell>Lincoln
 487:Douglas>Breckinridge>Bell>Lincoln
 448:Bell>Douglas>Lincoln>Breckinridge
 381:Bell>Douglas>Breckinridge>Lincoln
 256:Bell>Breckinridge>Douglas>Lincoln
 170:Bell>Lincoln>Douglas>Breckinridge
  22:Douglas>Breckinridge>Lincoln>Bell
  13:Breckinridge>Douglas>Lincoln>Bell
  11:Douglas>Lincoln>Breckinridge>Bell
   4:Bell>Breckinridge>Lincoln>Douglas

# 2000 American presidential election
11:Browne>Bush>Buchanan>Gore>Nader
 2:Buchanan>Bush>Browne>Nader>Gore
 8:Bush>Browne>Buchanan>Gore>Nader
16:Bush>Buchanan>Browne>Gore>Nader
12:Bush>Buchanan>Browne>Nader>Gore
17:Gore>Nader>Browne>Bush>Buchanan
 3:Nader>Browne>Gore>Bush>Buchanan
31:Nader>Gore>Browne>Bush>Buchanan

48:Gore>McCain>Bush
25:McCain>Bush>Gore
27:Bush>McCain>Gore

# Where to have a Tennessee state conference?
42:Memphis>Nashville>Chattanooga>Knoxville
26:Nashville>Chattanooga>Knoxville>Memphis
15:Chattanooga>Knoxville>Nashville>Memphis
17:Knoxville>Chattanooga>Nashville>Memphis

# Hare jumps to extremes on a left-right spectrum
18:FarLeft>Left>Center>Right>FarRight
16:Left>FarLeft>Center>Right>FarRight
17:Center>Left>Right>FarLeft>FarRight
 9:Center>Right>FarRight>Left>FarLeft
19:Right>FarRight>Center>Left>FarLeft
21:FarRight>Right>Center>Left>FarLeft

# Which team should have been Miami's opponent in the 2002 Rose Bowl?
 7788:Colorado>Nebraska>Oregon
10536:Colorado>Oregon>Nebraska
 6303:Nebraska>Colorado>Oregon
 5172:Nebraska>Oregon>Colorado
15248:Oregon>Colorado>Nebraska
 3838:Oregon>Nebraska>Colorado
# Yahoo! Sports conducted this ranked-ballot poll in late 2001.
# In the event, Miami played Nebraska and won 37-14.
# Oregon beat Colorado 38-16 in the Fiesta Bowl.

# EM list political party poll
Green>Democratic>Libertarian>NaturalLaw>Reform>Republican>Constitution
Green>Democratic>NaturalLaw>Libertarian>Reform>Republican>Constitution
Green>NaturalLaw>Democratic>Libertarian>Republican>Reform>Constitution
Libertarian>Constitution>Republican>Reform>Democratic>NaturalLaw>Green
Reform>Libertarian>Republican>Green>Democratic>Constitution>NaturalLaw
Republican>Libertarian>Democratic>Constitution>Reform>Green>NaturalLaw

32:Labour>Liberal>Conservative>SocialDemocrat
30:Conservative>Liberal>Labour>SocialDemocrat
23:SocialDemocrat>Liberal>Labour>Conservative
10:SocialDemocrat>Liberal>Conservative>Labour
3:Liberal>SocialDemocrat>Labour>Conservative
2:Liberal>SocialDemocrat>Conservative>Labour

# Demorep's silly Hare example
34:Hitler>Washington>Stalin
33:Stalin>Washington>Hitler
16:Washington>Hitler>Stalin
16:Washington>Stalin>Hitler

# Which game should we play?
Uno>TrivialPursuit>Scrabble>Life>poker>Risk>Yahtzee>Monopoly>BargainHunter>Pokerkub
Scrabble>Risk>Pokerkub>Yahtzee>poker>Life>Uno>Monopoly>TrivialPursuit>BargainHunter
TrivialPursuit>poker>Life>Scrabble>BargainHunter>Yahtzee>Pokerkub>Monopoly>Risk>Uno

# Bucklin and Woodall disagree
25:Brown>Jones>Davis>Smith
26:Davis>Smith>Brown>Jones
49:Jones>Smith>Brown>Davis

# Coombs and Hare are capricious
18:A>C>E>D>B
20:B>A>C>D>E
19:C>A>B>E>D
22:D>B>E>C>A
21:E>D>A>B>C

25:B>C>A>E>D
49:D>A>C>B>E
26:E>B>A>C>D

21:A>D>B>C
12:B>C>A>D
33:C>B>A>D
 6:C>D>B>A
25:D>A>B>C
 3:D>B>A>C

47:A>D>B>C
23:A>D>C>B
36:B>D>C>A
51:C>A>B>D
52:C>B>A>D
23:D>B>A>C
14:D>B>C>A

# Heitzig, Schulze and Tideman disagree
16:B>A>E>D>C
27:C>B>A>E>D
17:C>E>A>D>B
31:D>A>B>C>E
 9:E>D>B>C>A

# A is Borda-superior to Condorcet winner B
A>C>E>D>B
A>D>C>B>E
B>A>C>D>E
B>A>D>E>C
E>B>A>C>D

A>C>B>F>D>E
B>C>E>F>D>A
D>B>A>F>E>C
E>A>B>C>F>D
E>D>A>B>C>F
F>C>D>A>B>E

A>C>D>E>B
B>A>C>E>D
B>A>E>D>C
D>C>E>B>A

This ranked-ballot voting calculator was inspired in part by Rob Lanphier’s Pairwise Methods Demonstration; Lanphier maintains the Election Methods mailing list.  In turn, my calculator inspired Eric Gorr’s Condorcet Matrix.

Please e-mail any questions, problems or suggestions to rob@approvalvoting.org.


Back to Ranked-ballot voting methods

Robert Hampton “Honky” LeGrand III ’98