[EM] To Condorcetists:

Juho Laatu juho4880 at yahoo.co.uk
Tue May 22 00:48:28 PDT 2012


Here is a quick analysis of the proposed Approval strategy against the Approval example that I gave earlier.

I have two descriptions of the strategy. Their meaning should be the same.
- "Approve the candidates who are better than (or maybe exactly as good as) the result-merit that you expect from the election"
- “Would I rather appoint him/her to office than hold the election?”

Now let's see what will happen in the election where the voters have following approximate poll results (and/or general understanding of the preferences of the voters) available.
26: A > B >> C
26: B > A >> C
24: C >> A > B
24: C >> B > A

Note that if Approval election polls are collected as approvals, the voters wll have less information available for decision makin than this. They could know only the sum of approvals, e.g. A;52, B:52, C:48. But let's assume for now that they have more information that they can use as a basis for their strategic decisions.

First guess of the voters must be that either A or B will win. The expected outcome is between the values of A and B. If all the voters follow the given stratey they should vote as follows.
26: A
26: B
24: C, A
24: C, B

With these votes A or B wins. However, it is highly unlikely that voters will vote this way. The strategy allows the voters to take into consideration also the possible strategic votes. And the voters should take into accout possible changes in the opinions before the election day. Voters are also typically slightly optimistic in the sense that they have tendency to think that their own favourite candidates are better and more popular and will gain more votes before the election day than they actually will do in real life. Yet one more reason not to follow the stategy is interest to sen a message, e.g. by not approving A nor B (potential winners) in order to show that one does not support them. One may do this also in these elections in order to make a good start for the next elections.

One problem with the above listed votes is also that they do not measure the real opinion of the voters. If A will be more popular than B in the election day, that will not be mesured at all. Both have 50% chance to win even if people woul like to elect A. This is a falure of the method to measure the true opinions of the voters.

Second problem. The voters are not really on average this skilled in determining the expected outcomes. Many people will not follow the given strategy. My guess is that the most common deviation from the strategy is to cast shorter votes. In any case there will be a mixture of all kind of votes, not just votes that follow the strategy accurately.

Second try. Now the voters take some additional things into account when determining the expected outcome. C supporters are maybe the first to note that actually C could win. Since they prefer C strongly it doesn't take much to switch to bullet voting.
26: A
26: B
01: C, A
23: C
01: C, B
23: C

Now C wins. This is not a good result since A and B have majority. Most people and most methods agree that A or B should actually win.

Thirs try. Now A and B understand the probable behaviour of the C supporters and they realize that they can not follow their first strategy. Actually they can still vote in line with the strategy. Thy just assume that due to strategic voting (and possible changes in opinions) also C has a chance to win. Their expected outcome falls below the value of A and B.
26: A, B
26: B, A
01: C, A
23: C
01: C, B
23: C

Now A or B wins again. And still voters have no proper say on which one of them will win. The outcome will be a lottery, even if A is more popular than B. (The C voters may have some say here since some of them may approve A or B depending on how much they like them.)

One problem is that it is no likely that all A and B supporters will follow the strategy. Some of them simply fail to identify their best strategy and they may bullet vote either A or B, which easily allows C to win. (This problem exists also in other advanced methods but not as strongly.)

Further, A and B supporters have a strong incentive to bullet vote since few bullet votes will make their favourite win. But too many strategic votes make both their favourites lose. This means that Approval voters face a major dilemma. If we assume that A is slightly ahead of B in preference, A supporters that approve both may elect B, and A supporters that approve only A may elect C. There is no way the A supporters could vote rationally and safely and get the correct winner.

We can see that voters have also other (more offensive) working (but risky) strategies that they may mix with the recommended strategy.

If A and B come from the same party, a natural solution for the party (to fix the strategy problems) would be to nominate only one candidate. But if there are more than two potntially winning parties that can not give orders to each others (as usual), there may be more than three potential winner candidates in the election, and we may face the problems of this example. Even in Plurality elections there are often third party candidates although they are quite likely to be spoilers to the second favourite of their supporters.

It seems that with high probability in this election the voters will have great difficulties to follow the recommended strategy in a way that would pick the rightful winner. In theory the voters could be so skilled with estimating the expected outcome that they could even pick the rightful winnner (A, if A was in the end more popular than B). But in practice it looks like this will be a mess. My guess is that in real life elections C will win with highest probability since many enough A/B supporters will fail to approve both of their favourites.

The recommended strategy is likely to be too difficult for the voters to apply successfully. If they don't get confused with the strategy itself with sincere opinios from the poll, they probably will have difficulties in analyzing how others are likely to vote and how the opinions may change and how that should impacts their selection of their ideal strategic vote. In this set-up, to reach the rightful outcome, and for the A/B side to win, the A/B party/parties should publicly remind people that they should approve both A and B. That recommendation would however make the election pretty meaningless in the sense that nobody would indicate any preference on whether A or B should win (assuming that C party recommends, or its supporters themselves decide to bullet vote). The recommended strategy and Approval method don't seem to work well enough in this given set-up. Since three or more potential winners is the target situation, the strategy does not seem to be good enough in guaranteeing a rightful and rational outcome of the election.

The voters won't probably like the idea of having to make this kind of complex strategy decisions. Sincere voting (=approve the approvable candidates) would be one option, but we know that then the stratgic voters will have more weight than the sincere ones.

The promise of Approval (when compared to Plurality) is that it allows also third party candidates to run without becoming spoilers. And it works fine; it is ok to approva one of the two(!) frontrunners and all the third party candidates that one likes. But when the third parties grow and become potential winners, the toolbox of Approval voters is not sufficient, and the method will face problems like the one that was discussed above. For this reason, Approval may be a good start of a Plurality reform, but not a good long term solution.

Juho



On 21.5.2012, at 12.05, Juho Laatu wrote:

> On 20.5.2012, at 1.00, Michael Ossipoff wrote:
> 
>> You asked if I’d answer questions that you say remain unanswered. Of course. I answer all questions. If there’s a question that I haven’t answered, then let me know.
>>  
>> But please be specific.
> 
> Maybe the number one on the list of the still unanswered questions is the following one.
> 
> 
> [example+question starts here]
> 
> 26: A > B >> C
> 26: B > A >> C
> 24: C >> A > B
> 24: C >> B > A
> - A and B are Democrats and C is a Republican
> 
> How should voters vote after seeing these (quite reliable) poll results if they follow the "better than expectation" strategy? Should A and B be seen as the expected winners with 50% winning chance both? Maybe 50% of the voters should guess that A wins and 50% that B wins (?).
> 
> [example+question ends here]
> 
> 
> A good answer to this question would solve many of the Approval strategy related open questions. (Working Condorcet strategies still to be covered.)
> 
> What should an individual regular voter do in the given situation? How do they identify their best strategic vote?
> 
> That situation is quite common, except that accurate ties in polls are not common. In practice that could mean one poll saying that A leads B by 0.5% and another one saying that B leads A by 0.4%. Anyway, the difference between A and B falls within the error margin and expected amount of changes in opinions before the election day, and people are uncertain of which one of A and B will be more popular. If you want, you may assume that C is not likely to reach 50% first preference support.
> 
> Juho






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