Sunday, March 01, 2020

Ranked Voting ("Borda") -- almost works

When I presented Instant Run-off Voting to the students in my high school government class, one suggested that instead we choose the winner by awarding points based on place rank. In a race with 5 candidates, give first place 4 points, second place 3 points, third place 2 points, etc. It turns out, his idea is an old one, going back to at least the 1700s, when it was called "Borda voting."

Consider this outcome:


votes1st place2nd place3rd place
9Biden +18Warren +9 Sanders
8Sanders +16Biden +8Warren
7Warren +14Sanders +7Biden

By IRV, Warren is eliminated, and Sanders wins, 15:9 over Biden. By Ranked voting, the final count is Biden 26, Sanders 23, Warren 23, and Biden wins.

This certainly seems to represent the votes better than IRV. Or consider this:


votes1st place2nd place3rd place
9Biden +18Warren +9Sanders
8Sanders +16Warren +8Biden
1Warren +2Sanders +1Biden

The count is Biden 18, Sanders 17, Warren 19. Warren wins. Even though few wanted her for first place, everybody had her for first or second. Wouldn't this be a better outcome than the other options, where half the people would get their last choice?

For this reason, ranked voting favors candidates with broad appeal. Candidates that alienate 1/3 of the electorate will struggle against those who do well across the board, especially in races with more candidates.

Ranked voting does not suffer from the Love-Hate Paradox. Looking at the first example above, scoring 2 points for last place, the count would be Bernie 25, Warren 25, Biden 22: The candidate Ranked voting chooses first for "best" is chosen last for "worst." In the second example, the count is Bernie 19, Biden 18, Warren 17: again showing that the "best" candidate places last when choosing the "worst." Neither does the Participation Paradox function: there is no way that not voting will help your candidate.

Cloning

Now we get to Ranked voting weirdness. Consider this election for favorite color:
votes1st place (x3)2nd place (x2)3rd place (x1)4th place (x0)
4Yellow +12Red +8 Green +4Blue
3Red +9Green +6Yellow +3Blue
3Green +9Blue +6Yellow +3Red
2Blue +6Red +4Yellow +2Green
Red: 21 winner
Yellow: 20
Green: 19
Blue: 12

Fair enough. But what happens when olive green and pale green are added to the election, like this:

votes1st (x5)2nd (x4)3rd (x3)4th(x2)5th (x1)6th (x0)
4Yellow +20Red +16 Green +12Olive +8Pale +4Blue
3Red +15Green +12Olive +9Pale +6Yellow +3Blue
3Green +15Olive +12Pale +9Blue +6Yellow +3Red
2Blue +10Red +8Yellow 6Green +4Olive +2Pale
Green: 43 winner
Red: 39
Yellow:32
Olive: 31
Pale Green: 19
Blue:16

Nobody changed their opinion about whether they liked Red or Green better. But the addition of other green options to the election caused green to rise from 3rd place to 1st!

Weird, yes. But worse than "weird," because this means you can game the election. The winner becomes not so much who is the favored choice of the people, but who can best create this slate of candidates that will be consistently voted in an ordered block. An election of Conservative vs. Moderate vs Liberal 1, Liberal 2, and Liberal 3 will almost always go to Liberal 1. This is because when voters vote liberal, the best the Conservative or Moderate can do is 4th place, but where they don't vote liberal, the worst Liberal 1 can do is 3rd place.

Spoilers

Ranked voting is also subject to Spoiler effects. Suppose a candidate with no hope of winning draws some votes from Red. Pink perhaps:

votes1st place (x4)2nd place (x3)3rd place (x2)4th place (x1)5th place (x0)
4Yellow +16Pink +12 Red +8Green +4Blue
3Red +12Green +9Yellow +6Blue +3Pink
3Green +12Blue +9Yellow +6Red +3Pink
2Blue +8Red +6Yellow +4Green +2Pink
Yellow: 32 winner
Red: 29
Green: 27
Blue: 20
Pink: 12

Again, no one changed their opinion of Red, Green, or Yellow. But the 4 Yellow voters, by liking pink better than red, caused Yellow to win. 

Dark Horse voting

This is a "deliberate spoiler" trick, although it comes with risks. Yellow can use the hopeless Blue to win the election:
votes1st place (x3)2nd place (x2)3rd place (x1)4th place (x0)
3Yellow +9Blue +6 Red +3Green
1Yellow +3Red +2 Green +1Blue
3Red +9Green +6Yellow +3Blue
3Green +9Blue +6Yellow +3Red
2Blue +6Red +4Yellow +2Green
Yellow: 20 winner
Red: 18
Green: 16
Blue:18

Again, people's opinions of, and votes for Red vs. Yellow haven't changed. But by voting 2nd place for Blue, Yellow make Red lose. There is a natural limit to this game, obviously. If a couple Red voters had tried to do the same thing, Blue would have won, which was the least desirable outcome for the Red and Yellow voters. So people aren't likely to do it to extremes. Yet it is easy to imagine that on rare occasions, people will vote up an obvious loser who isn't as much a loser as they thought, and elect the candidate they most abhor.

Conclusion

Ranked voting has a number of advantages over IRV. It maintains the appearance of the winner being the actual favorite, and it doesn't produce contradictory results. However, it opens the door to lots of electoral gamesmanship. The last thing a worried electorate needs is an electoral system with candidates accusing each other of gaming the system.

Fortunately, there is yet another alternative. Next up: Range voting.

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