Voting systems

I was reading about voting systems, and realised that several appealing systems are considered single-winner. This confuses me, because for most of them, I can’t see what the problem is with extending them to multi-winner scenarios. For example, I find range voting intuitively appealing. What stops us from using that system to divide seats in parliament? We could add the scores of all the parties together, and then allot seats in proportion to the their share of the total. This sounds like a good system to me - suppose 45% of the voters vote for party A, with an average of 9/10, giving party B an average of 2/10, while the remaining voters give party B an average of 6/10, but party A 5/10. In this scenario, The supporters of party A are far more dedicated than the supporters of party B, and the latter seems to agree almost as much with A as B.
Isn’t a rated assessment much more valuable than just picking the one party you prefer to all others? Shouldn’t we be more interested in electing the party that people agree most with on average, rather than the one most choose as their favourite, when their second choice could be just as agreeable to many?

The problem with letting voters give nuanced scores to candidates (or parties or issues or whatever) is that you create an incentive for the voters to lie. For a nice simple example, let’s say that we have two candidates, a Whig and a Tory. The Whigs are in the majority (say, 55-45), but they’re easy to please: In actuality, a Whig would have a satisfaction of about 8 out of 10 for a Whig candidate, but only 7 out of 10 for a Tory candidate. The Tories, meanwhile, are iron-clad in their views: Any Tory voter will consider the Tory candidate to be a 10 out of 10, and a Whig to be 0 out of 10.

Now, in an ideal voting setup, the Tory would win in this situation, since you’ve got a country divided into people who definitely want him, and people who barely care. But those Whigs do care: Any given Whig would like it better if the Whig won, even if only a little. So if a Whig is voting rationally (that is, in a way that is most likely to give him as much as possible of what he wants), he’ll mark down on the ballot that the Whig is a 10 and the Tory is a 0, even though that’s not his real assessment of them.

An important feature of any voting system is that it be easily comprehensible. While it’s important for a vote to accurately reflect the will of the electorate, it’s just as important for the electorate to BELIEVE that their will is accurately reflected. The legitimacy of a government actually depends on the latter more that the former.

This is why clever and complex voting systems are rarely a good idea. While they may provide a result that is theoretically more in line with what the voters actually want, the resulting reduction in confidence in the fairness of the system isn’t worth it.

Kenneth J. Arrow won the Nobel Prize for (in part) showing that ANY election system will break down in particular circumstances. No conceivable system will work in all circumstances.

One of the “graveyards” of election systems is a highly polarized electorate. If 49% lean conservative, and 49% lean liberal, then there is a terrible rush for each side to appeal to even the most extreme third party, if it can push them ahead of the opposition in a coalition. You get the tail wagging the dog…

Other horrors are non-transitive systems, strategic voting systems (you gain power by voting for someone you don’t want to win!) and systems that are not independent of irrelevant alternatives.

(The classic example of that goes as follows…
A: Would you like chocolate or vanilla?
B: I’ll have chocolate.
A: Oh, I see we also have strawberry.
B: Well, in that case I’ll have vanilla.
A: I’m sorry, I was wrong, we’re out of strawberry.
B: Then I guess I will have chocolate.)

It sounds absurd…until we remember the Perot and Nader campaigns…

Trinopus

The statement of Arrow’s theorem is a bit more qualified than “any voting system”. There are stronger impossibility theorems these days, but I don’t know of any that apply to any voting system.

I was thinking about this… is an incentive to lie necessarily a bad thing? Imagine if everyone lied about their second choice, giving it 0 out of 10 - in that case you would still just end up with a ‘normal’ one-party vote, not anything worse than that. So it seems to me that liars can’t decrease the accuracy below one-party votes, but honest voters can increase it. Also, the more people care to lie, the less it is likely to matter - Imagine a voter who’s 8/10 Whig and 7/10 Tory - he still likes the Tories pretty good, so he’s got good reason to actually give them a good rating so that even if the Whigs don’t win, at least those pesky Bedfordites won’t. Then there’s another voter, 8/10 Whig and 2/10 Tory - he likes the Tories little enough to lie and vote 0/10, but then the difference is only slight, not like if he lied them down from 7/10.

I’m not so sure about The Hamster King’s objection either - I think it would give me confidence to know that I had been given the opportunity to express my opinion more accurately. I’m a support member of one party, but I still feel strongly for my second choice, and would much like the opportunity to vote for them as well - and also, an opportunity to really rate down a couple parties I don’t like at all.

I don’t know that I agree that they necessarily result in less confidence in the fairness of the system. Ireland has a notoriously complicated system, and yet having lived both here and in the US for considerable periods of time, I don’t see any indications that people here think the system is less fair. I actually think that any proposals to simplify it would be strenuously rejected precisely because people would think that would make it less fair.