From http://electionmethods.org/evaluation.htm
Winner 0 is A, 1 is B, ...
A vote "A,C" means ranking "A" highest, "C" next, and any remaining candidates equivalently last. These rankings were represented as preferences with real numbers from 1.0 to -1.0, either {1.0, 0.0, -1.0} for 3 candidates or {1.0, .33, -.33, -1.0} for 4 candidates.
Exhibit A, IRV gets the wrong answer.
17 voters, 3 candidates 8: A,C 5: B,A 4: C,B
| Method | Happiness | Winner |
|---|---|---|
| Max Happiness | 0.235294117647059 | 0 |
| One Vote | 0.235294117647059 | 0 |
| Instant Runoff Vote | -0.176470588235294 | 1 |
| Acceptance Vote | 0.235294117647059 | 0 |
| Rated Vote, raw | 0.235294117647059 | 0 |
| Rated Vote, equal sum | 0.235294117647059 | 0 |
| Rated Vote, maximized | 0.235294117647059 | 0 |
| Rated Vote, 1..num choinces | 0.235294117647059 | 0 |
| Rated Vote, 1..10 | 0.235294117647059 | 0 |
| Ranked Vote | 0.235294117647059 | 0 |
| Ranked Vote, no neg pref | 0.235294117647059 | 0 |
| Condorcet | 0.235294117647059 | 0 |
| IRNR | 0.235294117647059 | 0 |
| Random | -0.0588235294117647 | 2 |
Just like A, but as if two of the 8 "A,C" voters change their mind to like "C" better. Counterintuitively, this causes the IRV winner to change from "B" to "A". A was devalued over the previous example, but now wins. (nevermind this happens to be the "right" answer, it's supposed to point out how flakey IRV is)
17 voters, 3 candidates 6: A,C 5: B,A 4: C,B 2: C,A
| Method | Happiness | Winner |
|---|---|---|
| Max Happiness | 0.117647058823529 | 0 |
| One Vote | 0.117647058823529 | 0 |
| Instant Runoff Vote | 0.117647058823529 | 0 |
| Acceptance Vote | 0.117647058823529 | 0 |
| Rated Vote, raw | 0.117647058823529 | 0 |
| Rated Vote, equal sum | 0.117647058823529 | 0 |
| Rated Vote, maximized | 0.117647058823529 | 0 |
| Rated Vote, 1..num choinces | 0.117647058823529 | 0 |
| Rated Vote, 1..10 | 0.117647058823529 | 0 |
| Ranked Vote | 0.117647058823529 | 0 |
| Ranked Vote, no neg pref | 0.117647058823529 | 0 |
| Condorcet | 0.117647058823529 | 0 |
| IRNR | 0.117647058823529 | 0 |
| Random | 0.0588235294117647 | 2 |
Another example IRV gets wrong
21 voters, 4 candidates 7: A,B,C 6: B,A,C 5: C,B,A 3: D,C,B
| Method | Happiness | Winner |
|---|---|---|
| Max Happiness | 0.427142862762724 | 1 |
| One Vote | 0.206190476814906 | 0 |
| Instant Runoff Vote | 0.206190476814906 | 0 |
| Acceptance Vote | 0.427142862762724 | 1 |
| Rated Vote, raw | 0.427142862762724 | 1 |
| Rated Vote, equal sum | 0.427142862762724 | 1 |
| Rated Vote, maximized | 0.427142862762724 | 1 |
| Rated Vote, 1..num choinces | 0.427142862762724 | 1 |
| Rated Vote, 1..10 | 0.427142862762724 | 1 |
| Ranked Vote | 0.427142862762724 | 1 |
| Ranked Vote, no neg pref | 0.427142862762724 | 1 |
| Condorcet | 0.427142862762724 | 1 |
| IRNR | 0.427142862762724 | 1 |
| Random | 0.427142862762724 | 1 |
Another example IRV gets wrong
20 voters, 3 candidates 8: A,B 7: C,B 5: B
| Method | Happiness | Winner |
|---|---|---|
| Max Happiness | 0.25 | 1 |
| One Vote | -0.2 | 0 |
| Instant Runoff Vote | -0.2 | 0 |
| Acceptance Vote | -0.2 | 0 |
| Rated Vote, raw | 0.25 | 1 |
| Rated Vote, equal sum | 0.25 | 1 |
| Rated Vote, maximized | 0.25 | 1 |
| Rated Vote, 1..num choinces | 0.25 | 1 |
| Rated Vote, 1..10 | 0.25 | 1 |
| Ranked Vote | 0.25 | 1 |
| Ranked Vote, no neg pref | 0.25 | 1 |
| Condorcet | 0.25 | 1 |
| IRNR | 0.25 | 1 |
| Random | -0.3 | 2 |
From a presentation slide by Dr. Donald Saari, UC Irvine. Demonstrating the dismal situration where three different outcomes are possible depending on the elecetion system.
20 voters, 4 choices 2: A,B,C,D 1: A,C,D,B 2: A,D,C,B 2: C,B,D,A 3: D,B,C,A
| Method | Happiness | Winner |
|---|---|---|
| Max Happiness | 0.0666669994592667 | 3 |
| One Vote | 0 | 0 |
| Instant Runoff Vote | 0 | 0 |
| Acceptance Vote | -0.0666689962148666 | 1 |
| Rated Vote, raw | 0.0666669994592667 | 3 |
| Rated Vote, equal sum | 0.0666669994592667 | 3 |
| Rated Vote, maximized | 0.0666669994592667 | 3 |
| Rated Vote, 1..num choinces | 0.0666669994592667 | 3 |
| Rated Vote, 1..10 | 0.0666669994592667 | 3 |
| Ranked Vote | 0.0666669994592667 | 3 |
| Ranked Vote, no neg pref | -0.0666689962148666 | 1 |
| Condorcet | 0 | 0 |
| IRNR | 0.0666669994592667 | 3 |
| Random | -0.0666689962148666 | 1 |
The "Milk,Beer,Wine" example. Any of the 3 possible outcomes can happen depending on the system.
15 voters, 3 choices 6: A,C,B 5: B,C,A 4: C,B,A
| Method | Happiness | Winner |
|---|---|---|
| Max Happiness | 0.266666666666667 | 2 |
| One Vote | -0.2 | 0 |
| Instant Runoff Vote | -0.0666666666666667 | 1 |
| Acceptance Vote | -0.2 | 0 |
| Rated Vote, raw | 0.266666666666667 | 2 |
| Rated Vote, equal sum | 0.266666666666667 | 2 |
| Rated Vote, maximized | 0.266666666666667 | 2 |
| Rated Vote, 1..num choinces | 0.266666666666667 | 2 |
| Rated Vote, 1..10 | 0.266666666666667 | 2 |
| Ranked Vote | 0.266666666666667 | 2 |
| Ranked Vote, no neg pref | 0.266666666666667 | 2 |
| Condorcet | 0.266666666666667 | 2 |
| IRNR | 0.266666666666667 | 2 |
| Random | 0.266666666666667 | 2 |
A thought experiment I saw out there on the net.
winner 0 = Dean, 1 = Gephardt, 2 = Edwards, 3 = Lieberman, 4 = Clark
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
| Method | Happiness | Winner |
|---|---|---|
| Max Happiness | 0.235 | 1 |
| One Vote | -0.34 | 0 |
| Instant Runoff Vote | -0.03 | 3 |
| Acceptance Vote | 0.235 | 1 |
| Rated Vote, raw | 0.235 | 1 |
| Rated Vote, equal sum | 0.235 | 1 |
| Rated Vote, maximized | 0.235 | 1 |
| Rated Vote, 1..num choinces | 0.235 | 1 |
| Rated Vote, 1..10 | 0.235 | 1 |
| Ranked Vote | 0.235 | 1 |
| Ranked Vote, no neg pref | 0.22 | 2 |
| Condorcet | 0.22 | 2 |
| IRNR | 0.22 | 2 |
| Random | -0.03 | 3 |