[EM] Single-winner method with strong winners (was: Poll for favorite single winner voting system with OpaVote)

[Juho Laatu]

In order to back up my comments on problems with replacing plurality with Condorcet here are also some requirements and one example method that could be used when we want to keep single-member districts and the idea that the strongest party wins, but still allow also other than the leading two parties/candidates to run without having problems with the lesser-of-2-evils problem.



Let's see first what kind of methods would be ideal.
- start from a two-party (few-party, single-seat) system and FPTP / Plurality
- make the necessary modifications
  1) allow third parties to run without becoming spoilers
  2) allow third parties to win only after they have become the "strongest party" of the district (i.e. not when they are just a compromise between two major parties)
- rule 2 eliminates the "weak Condorcet winner problem"
- use of FPTP / Plurality in an environment that allows only two parties is the ideal method for a pure two-party system
- the modified system is a few-party system, that allows the leading parties to change
- because of rules 1 and 2, opinion C>A>B, where C is a minor party, should have the same effect as opinion A>B
- IRV / single winner STV / Alternative Vote is one quite natural (but not perfect) approach to meeting requirements 1 and 2
- but because of problems related to its serial elimination order we introduce a third requirement / rule
  3) the method should be free of random variation like the impact of elimination order and addition/removal of clearly non-winning candidates
- the method can be used both for electing one single winner (e.g. a president) and for electing winners in each single-winner district
- for clarity we add one more (anti) requirement
  4) there is no requirement of country wide proportionality
- i.e. let the strongest candidate win in each district
-- end of requirements part ---

I went through a number of election methods that might meet these criteria well enough. I'll present one that is quite simple, except that it uses explicit approval, which makes voting a bit more complex than in basic IRV or Condorcet.

Use a Condorcet method to elect the winner among the most approved candidate pair and those who are at least as approved as the less approved of those two.
- a pair of candidates is approved by a voter if she approves at least one of those candidates

This method is summable. One should sum up information about pairwise comparisons, pair approvals and individual approvals.

20: A1 > A2 >>
15: A2 > A1 >>
33: B >> C
32: C >> B

In this example we have three major parties, A, B and C. Or alternatively we have four parties. In that case parties A1 and A2 are ideologically close to each others.

This method elects B since pair A1, B (or A2, B) is the most approved pair (approved by 68 voters), A2 is more approved than B, and B beats both A1 and A2 in pairwise comparison.

Note that if this method would pick the winner among the two most approved candidates (A1, A2), A1 would win.

In this example rule 1 is met quite well since C didn't spoil B's chances to win. Also A2 did no harm to A1.

Party C could be a new growing party. If it had already grown larger than party B, it would have won. Now it is still too small to win (the influence of rule 2 reaches up to this level).

Even if party A supporters would prefer C to B (but not approve them), C would still not win. It would still be classified as a "too weak compromise candidate". Few more votes would change this situation though.

Rule 3 should be ok now since there is no sequential process to eliminate the candidates (or other dubious practices). This method could in a way be said to jump directly to the last comparison of IRV (but hopefully in a sophisticated and sensible way). But wait a minute, use of the most approved pair is a dubious practice. Added and removed minor candidates may influence the outcome if those candidates are approved widely enough. But that would make them already major candidates, right?

Use of approvals typically requires a (sincere) strategy. In this method the voters should try to impact on which two candidates will be at least as approved as the most approved pair of candidates. That means that it would make sense to approve at least one candidate with reasonable chances to be among the most approved candidates (and not to approve too many of the candidates).

Does this method work well enough? Are this kind of methods useful methods in general?

If explicit approvals are too tedious for the voters, one could consider implicit approval of ranked candidates (there are however some problems, like inability of B and C supporters to indicate preference between A1 and A2) or implicit approval of the first candidate (there are however some problems, closely related candidates like A1 and A2 would be unable to support each others with approvals).

This method is not totally free of the strategy problems of approval. If competition between A1 and A2 is fierce, they might start dropping approvals of the other one of them, trying to reduce the approval level of the other one below the approval level of B. The strategic incentive is however weaker than in Approval since the final decision between A1 and A2 will be made using Condorcet if both of them are approved enough. Voters may thus be better off by maximizing the approval of both A1 and A2 (to stay ahead of B and C) and by being happy with the (fair) Condorcet decision between A1 and A2 (in the case that one of them will be the winner).

One could also have some strategy related problems when we have two major candidates (A, B) and one weak Condorcet winner between them (C). Supporters of A may start approving C if they are afraid that B will otherwise win. The sincere votes could be 47 B>>C>A, 47 A>>C>B, 6 C>>B>A. But even if 40 of the A supporters approve C, that is not enough.

The idea of this method was to elect the strongest candidate of the strongest party of each (or the only) single-member district, and avoid the lesser-of-2-evils problem and the spoiler problem, and avoid electing candidates from groupings/parties that are clearly smaller than the leading ones. The  rough philosophy can be said to be to wait with the third parties as long as they grow as strong (measured as approvals, which is related to but not the same as first preference support) as the previous leading two parties.

Juho



On 16.10.2011, at 1.08, Juho Laatu wrote:

> On 15.10.2011, at 23.24, MIKE OSSIPOFF wrote:
> 
>> Another "Oops!". I've just realized that I posted my most recent message to the wrong
>> thread. So now I'm posting it to the right thread:
>> .
>> Oops! I forgot that B voters ranked C. 
>> .
>> Yes, C wins, even though C has a very low Plurality score. 
>> .
>> But PC isn't intended to be Plurality. In fact, none of us want Plurality, 
>> so why should we use it for the standard for evaluating propoed 
>> replacemens for it? Plurality is not what we want.
> 
> In addition to plurality related problems that example addresses also some other problems. If we consider the C voters to be just noise (only 3 of them) and the A and B votes reflect the true opinion of the voters, then the votes are 49 A, 48 B > C. That looks like nearly a tie between A and B. In this situation the unanimous opinion of those who said something about B vs C is that B is better. It is strange that those 3 votes can turn the situation upside down. But the details are not that important. I just wanted to point out that also this method makes sometimes weird decisions.
> 
>> .
>> We don't say, "Don't vote for candidate X, because he isn't enough like
>> the incumbant"
>> .
>> After all, if agreement with Plurality us which results are better than others, then
>> wouldn't that imply that we should keep Plurality instead of replacing it?
>> .
>> We propose methods that meet criteria that are important to us, methods
>> that do important things that we prefer.
> 
> I agree with "things that we prefer" but not with "meet criteria that are important to us". The reason is that criteria tend to be black and white, and we know that we need to violate some good criteria anyway. That may well sum up to a method that violates numerous criteria that we like, but it might violate each one only a little bit. And the end result might be the best possible, although we violated most of the (good) criteria that were under consideration.
> 
>> For me, that means getting
>> rid of Plurality's lesser-of-2-evils problem as well as possible. PC and
>> MMPO do so excellently.
> 
> Yes, if we have plurality and we want to allow more than two parties/candidates to run, then it would be nice to get rid of the lesser-of-2-evils problem. I'm however often confused about what do people want to have in this situation.
> 
> In presidential elections my additional question is if it is ok to elect candidates that are a compromise between two major parties but that do not have a strong party and lots of first preferences behind them. If that is ok, then all classical Condorcet methods work fine (with sincere votes at least).
> 
> This problem is a bit more difficult if we start using Condorcet to elect representatives in single-member districts. Is it ok if the method is not proportional at all but could in principle give most of the seats to a centrist party with only few first preference supporters. If the answer is yes, then we are probably building a political system that wants to avoid proportional representation as well as the traditional two-party system and wants instead to focus on simply electing good individual representatives. This is not a common approach in building political systems.
> 
> Alternatives to this approach could be to try to implement proportional representation or to keep the idea that the strongest party should win in each single-member district, but now without the lesser-of-2-evils problem.
> 
> My point is just that if we want to replace plurality in some elections we should also state what kind of outcome we want. Replacing plurality with Condorcet (although Condorcet methods are good general purpose single-winner methods) may not make the system any better (maybe worse). I need targets before I can say if Condorcet is better than plurality in some particular situation.
> 
> Juho
> 
> 
> 
>>  
>> Mike 
>> 
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> 
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