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PAINT CHIPS: I merged these posts with the redistricting stuff to clean out the other threads. Voting systems stuff starts here, redistricting stuff starts with my posts.

Last edited by Paint CHiPs on 06-29-2006 at 08:27 PM

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It might well be the best system according to some orders of merit, but 'can't be improved on' in general probably isn't true, because different people want different things from their voting system.

I think that you need to say what your decider is in order to show that your system is the same as single-transferrable-vote, say. Would you pick the candidate that wins the most head-to-heads and then break ties with the head-to-head results? What if you had three equal candidates on total head-to-heads and their head-to-head results against each other were cyclic, so that each one beat another one once?.

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quote:

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Originally posted by Smug Git

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For example: some people want a voting system that provides 'strong government' (example: a first-past-the-post system). Others like a a more representative system (example: proportional representation), which tends to produce coalitions. Single transferrable vote, of course, can be used in both systems that I mentioned. However, there's more to it than 'we need to elect someone'; you could do that by lottery (which would fail the test according to your order of merit, whatever it is, I suspect). Modern technology offers new voting methods (because the sort of system that you're talking about would not have been very computationally feasible not that long ago).

Anyhow, for your order of merit, you'd have to define 'want the most', I guess (it sounds to some extent that you could equally well mean 'most people want' with 'want' suitably qualified).

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quote:

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Originally posted by Smug Git
[B]For example: some people want a voting system that provides 'strong government' (example: a first-past-the-post system). Others like a a more representative system (example: proportional representation), which tends to produce coalitions. Single transferrable vote, of course, can be used in both systems that I mentioned.

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Last edited by BROKEN_LADDER on 06-28-2006 at 10:43 PM

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I understood what you had in mind for a voting system without the example.

However, you perhaps misunderstand the point of PR systems; there is more than just 'wanting your guy' in office, there is also the matter of who you don't want in office. Coalitions limit the chance that your guy will have total control but also limit the chance that the guys that you don't like will have total control. PR isn't something that you'd use for Presidential elections, however, because there is only to be one President (even in your system, more than one president at once is very unlikely).

I don't think that people do want the same things from an electoral system. In particular, people can want more out of it than their candidate win; they might want them to be fair and/or representative, for example (regardless of who wins).

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quote:

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Originally posted by Smug Git
...you perhaps misunderstand the point of PR systems; there is more than just 'wanting your guy' in office, there is also the matter of who you don't want in office.

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There is such a thing as 'do or don't want'; you could want someone not to get into office enough to vote for someone that you don't really want in office because they have the best chance of winning. It's either not linear or it's linear but has negative values. 'Anyone but Bush' as a vote would appear to achieve that, but I need to think about whether it's the same.

With regards to you smacking your forehead, I was talking about elections, not candidates.

If you wish to make claims of perfection, you needs define your terms with more exactitude. I'm not really bothering to address your claims of perfection not because I agree with them, but because I don't see exactly what you're after nor, indeed, do I believe that there is only criterion for order of merit, absent a logical proof.

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Also, I'm not particularly sure that your system would work so well in a party-based parliamentary system (most countries don't directly elect a powerful president).

In any case, I'd prefer single transferrable vote; it's simpler, if nothing else.

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ah! i've found it! the system i'm talking about has already been discovered (which seems logical with all those math geeks throughout history), and is called "condorcet" voting, named after some guy called condorcet. as it turns out, i was wrong that this produces the same results as instant run-off voting; IRV has flaws, which the example i found on this page shows:

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Condorcet voting analyzes the one-on-one matchups of all the candidates by looking at the rankings. Here is a good example that I came up with. Say that you have an election with a right-wing extremist, a left-wing extremist, and a centrist:

25 million people vote for the centrist

35 million people vote for the right wing, then the centrist

40 million people vote for the left wing, then the centrist

Doesn't it seem the centrist should win? In Condorcet voting, the centrist wins. 65 million people prefer him to the right wing, 60 million prefer him to the left wing. In IRV, the centrist is eliminated first, and the left-wing candidate wins with less than half of the votes compared to the number of people voting.

There are other simple scenarios that just as easily demonstrate Condorcet's superiority over Approval and Borda.

Curt Siffert
Portland, Ore.

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Last edited by BROKEN_LADDER on 06-29-2006 at 12:51 AM

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That sort of system is just going to produce centrists, I would think, at least if there aren't that many serious candidates (not just from that example but in general). Is that a good thing? The IRV system gives heavier weight, in effect, to first choices, I guess.

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ah crap...but then there is this little matter to consider:

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Irrelevant Alternatives in Ranked Pairs

Arrow felt, that the addition of an alternative (or candidate) that doesn't win shouldn't affect the outcome. He called such an alternative an irrelevant alternative, and the property he was looking for "independence from irrelevant alternatives". Since this isn't satisfiable it's worth considering if these alternatives are truly irrelevant.

40 A C
60 C A

C is the Ranked Pairs winner here. But with the introduction of B, we get

40 A B C
35 B C A
25 C A B

And A is the Ranked Pairs winner. So, from the Ranked Pairs perspective, the introduction of B and the new information provided is decisive. What is that new information? Well, we know no that there is an alternative that beats C. We know that this alternative is beaten by A. In the A vs C example, all we knew was that most people preferred C to A.

Now, we have contradictory information from the fact that A is preferred to B and B is preferred to C. So, it isn't a surprise that this might tip the weight of evidence in favour of A.

source

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quote:

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Originally posted by Smug Git
That sort of system is just going to produce centrists, I would think, at least if there aren't that many serious candidates (not just from that example but in general).

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ahh! now i finally get it. this page explains it beautifully: http://condorcet.org/rp/arrow.shtml

the way arrow proved that no voting method--not just no voting method he could think of--could be perfect, is he literally showed an example of a three-candidate election where, no matter which candidate you pick, you violate rules which seem to be reasonable expectations for any voting system. so maybe he's really onto something here, in which case we're fucked. ack.

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If you can draw a line through candidates, centrists would be preferred by the system because of people's second choices; if nothing else, it'd be driven by edge effects. Of course, you can't really draw a line through the candidates, but as a first order approximation it has some merit, I think, if only because a lot of voters tend to think that way.

Applying equal weight to all choices doesn't make any more sense than any other weighting system, so far as I can see; it's a matter of preference. If you wanted to be fair, let people select their own weightings (mind you, many people probably can't do the mental arithmetic).

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quote:

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Originally posted by BROKEN_LADDER
ahh! now i finally get it. this page explains it beautifully: http://condorcet.org/rp/arrow.shtml

the way arrow proved that no voting method--not just no voting method he could think of--could be perfect, is he literally showed an example of a three-candidate election where, no matter which candidate you pick, you violate rules which seem to be reasonable expectations for any voting system. so maybe he's really onto something here, in which case we're fucked. ack.

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quote:

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Originally posted by Smug Git
If you can draw a line through candidates, centrists would be preferred by the system because of people's second choices; if nothing else, it'd be driven by edge effects. Of course, you can't really draw a line through the candidates, but as a first order approximation it has some merit, I think, if only because a lot of voters tend to think that way.

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Last edited by BROKEN_LADDER on 06-29-2006 at 01:33 AM

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quote:

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Originally posted by Smug Git
That's not really surprising when you draw from the set of 'what seems reasonable', because it seems to me that that's not, a priori, likely to be a consistent set. That's why you need an 'order of merit'; broadly, you decide how much you're happy to fulfil some criteria and how unhappy you are to miss others (that effectively comprises your 'cost function' in linear programming) and then try to reach the least worst solution.

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Simplified: I am saying then when designing an electoral system, you have constraints. You also have a set of what you feel to be 'reasonable objectives'. You might not be able to achieve them all. You therefore have to associate a 'cost' with achieving each one to whatever degree you can achieve it. In mathematics you can do this sort of thing exactly, eg, with Linear Programming.

Again, I am talking about designing an electoral system. The order of merit is about how you pick an electoral system, not a candidate within a settled electoral system.

This approach to problems isn't novel, incidentally. It's the sort of thing you have to do when you have conflicting imperatives.

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