voting example

[mindstalk]

Poll on an imaginary election:

34 A > S > B > C
32 B > S > C > A
33 C > S > A > B
1 S > A > B > C

Of the four candidates, which do you think should win?

Comments

[mtbc]

This is why I like approval voting; ranks make it too confusing for me to decide what to do! (But, given ranks, my default answer is probably: whatever the Debian folks would do. (-:)

[elusiveat]

Occasionally when I am casting a vote for city council where you're supposed to vote for up to four candidates I find myself wondering if the strategic thing to do is to vote *only* for the non-incumbent candidate that I like, even though I also like several of the incumbents, on the basis that any vote I cast for a incumbent is likely to push my favorite person further down in the heap.

I feel like there could be a similar potential for trying to game the system with approval voting, although I have not checked how the numbers work out.

[mindstalk]

Strategic voting for approval is to vote for your favorite, and also for your preferred of the top two in polls, if different (and if you have reasonably reliable opinion polls). Never hurts to vote for favourite but if they're not likely to win you can influence the actual winner.

[mindstalk]

Debian would choose S, I think; they seem to use Schulze, which is a Condorcet method, and S is the Condorcet winner here.

[mtbc]

Ah, cool, thank you. It's usually at around the Schwartz set stuff in https://www.debian.org/devel/constitution#item-A that my eyes glaze over. (In this case I don't think we need that part.)

[kgbooklog]

Who shuold win, or who WOULD win? The latter is C, 65 to 35 over A in the last round.

Most of the confusion comes from the lines being listed out of order.

[elusiveat]

I'm pretty sure that who *would* win depends on what voting system you're using. Mindstalk didn't specify.

[mindstalk]

I don't know what you mean by out of order or confusion.

[elusiveat]

Probably needs some preference magnitudes to really be obvious, but I do see the case for S over A.

[kgbooklog]

I was assuming Instant Runoff, but if candidates are assigned points based on their ranking on each ballot, then I would expect S to win.

A only wins in First Past the Post.

[elusiveat]

When I first looked over the options I kind of glossed the fact that almost no one was included in the last line.

[mindstalk]

There are many ways of counting ranked ballots. IRV is currently popular despite being terrible. Points would be Borda Count which is apparently gameable by the candidates.

Another is Condorcet, looking at pairwise matchups. S clearly beats all the other candidates one on one.

[elusiveat]

Condorcet or bust?

[come_to_think]

Keep in mind Arrow's impossibility theorem: There is *no* voting system that satisfies a short list of plausible-looking, indeed weak-looking, requirements.

[mindstalk]

No ranked system anyway. There seems debate about score voting.

But that doesn't mean all the systems are equally bad, else we wouldn't bother trying to replace plurality. And I think the proof is less about system flaws than the nature of collective preference. There may not be a Condorcet winner and then the right choice isn't obvious. But IRV doesn't even pick a Condorcet winner when one clearly exists.