Ranked-ballot voting calculator
This form calculates the winners of several ranked-ballot voting methods.
See below for input examples.
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 whether 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 |
# 2004 American Democratic primary |
33:Dean>Gephardt>Edwards>Lieberman>Clark |
22:Clark>Edwards>Gephardt>Lieberman>Dean |
18:Lieberman>Clark>Edwards>Gephardt>Dean |
16:Gephardt>Lieberman>Edwards>Clark>Dean |
7:Edwards>Clark>Gephardt>Lieberman>Dean |
4:Edwards>Lieberman>Gephardt>Clark>Dean |
# 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 |
# sometimes it's better to be eliminated early rather than late under Hare |
13:Libertarian>Right>Left>Statist |
15:Libertarian>Left>Right>Statist |
14:Left>Libertarian>Statist>Right |
12:Left>Statist>Libertarian>Right |
12:Statist>Left>Right>Libertarian |
10:Statist>Right>Left>Libertarian |
11:Right>Statist>Libertarian>Left |
13:Right>Libertarian>Statist>Left |
# These preferences are consistent with the Nolan chart. |
# Try adding 3 more Statist>Right>Left>Libertarian ballots. |
# Or, try deleting 3 Right>Statist>Libertarian>Left ballots. |
# 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. |
# three yes/no issues in order of importance |
600:NNN>NNY>NYN>YNN>NYY>YNY>YYN>YYY |
300:NYY>NYN>NNY>YYY>NNN>YYN>YNY>YNN |
302:YNY>YNN>YYY>NNY>YYN>NNN>NYY>NYN |
303:YYN>YYY>YNN>NYN>YNY>NYY>NNN>NNY |
# three large special-interest groups |
300:NNN>NNY>NYN>YNN>NYY>YNY>YYN>YYY |
301:NNY>NYY>YNY>YYY>NNN>NYN>YNN>YYN |
303:NYN>NYY>YYN>YYY>NNN>NNY>YNN>YNY |
307:YNN>YNY>YYN>YYY>NNN>NNY>NYN>NYY |
# 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 |
# 1969 referendum on name of new city created from Fort William and Port Arthur, Ontario |
10256:ThunderBay>Lakehead>TheLakehead |
5614:ThunderBay>TheLakehead>Lakehead |
15302:Lakehead>TheLakehead>ThunderBay |
8377:TheLakehead>Lakehead>ThunderBay |
# Thunder Bay won real referendum with a plurality |
# 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 |
PizzaHut>PapaJohns>Dominos>LittleCaesars>CaliforniaPizzaKitchen |
Dominos>LittleCaesars>CaliforniaPizzaKitchen>PizzaHut>PapaJohns |
PapaJohns>Dominos>LittleCaesars>PizzaHut>CaliforniaPizzaKitchen |
Dominos>PizzaHut>PapaJohns>LittleCaesars>CaliforniaPizzaKitchen |
PapaJohns>Dominos>PizzaHut>CaliforniaPizzaKitchen>LittleCaesars |
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 Voting Calculator.
Please e-mail any questions, problems or suggestions to approval98@gmail.com.
Back to Ranked-ballot voting methods