[EM] To Condorcetists:

[Juho Laatu]

On 21.5.2012, at 18.03, Abd ul-Rahman Lomax wrote:

> Drive-by comment.
> 
> At 04:05 AM 5/21/2012, 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.
> 
> If this is the most important unanswered question, you are lucky, Juho.

A good point to start the analysis.

> 
>> [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]
> 
> This is an unanswerable question about a preposterous situation, that *will not* occur in real public elections under conditions where elections even make sense. The population is entirely and completely polarized into two camps of almost equal size. No voters are intermediate in position, no voters have C as their second favorite. Essentially, there are no "independent" voters.

There can be also additional candidates and richer set of voter opinions. However the general set-up where one wing has two srong candidates, the other one has one, and the balance between the wings is close to 50%-50%, is a common se-up that all good methods should be able to handle. This example ignores the finer details in order to show the core concepts (three major candidates and their relative position).

> 
> Now, suppose that, nevertheless, we have such a situation. The problem boils down to two parties, with one having a slight edge over the other. The other, the slight majority party, is united. The majority party is itself evenly divided into two factions, supporters of A and B.

Yes.

> Do they care about winning? From the stated preferences, yes, that is what >> means. Strong preference.

I assume that this is a competitive election (with or without the strong >> preferences).

> If they care about winning, they will never let this situation go to an election, they will present a united candidate, even if they have to toss a coin to do it.

If Approval can not handle three potential winners, then making sure already before the election that there will be only two potential winners would make the common Approval strategies work. Often we don't have this luxury. The other Democrat candidate could as well be from a rival Democrat2 party.

> 
> That is what the Democrats *must* do if the method is plurality. That is why Plurality leads to 2-party systems. What is presented here is really a three party system, with the slight majority party being split into two factions. Parties that allow themselves to be split this way lose elections.

Yes, this example could be from a society with three or more (potentially winning) parties.

> 
> Society itself, overall, it this situation, doesn't give a hoot. The SU of all three winners is evenly divided.
> 
> So from what perspective do you want to advise voters? For obtaining their individually-maximized utility? Or for creating a socially beneficial result, which indirectly benefits *all* individuals, because a coherent society produces value for all members?

I assume that the election is competitive. So the individual voters want an answer to questions "how can I make my favourite candidate win" and "how can I make my favourite party/wing win".

> 
> So, next step up with improved voting system, what about Approval? From the stated preferences, A and B voters have a dilemma, but it is only a small one. If they do not unite, they risk losing to C, a big loss. If they do unite, they risk their favorite losing to their next-favorite, but by the terms of the problem, this is a smaller loss. They maximize expected personal utility by approving both A and B.
> 
> If they get greedy, and only go for their favorite, they risk loss to the least-favorite, by far. They would, basically, deserve this loss. The reward of greedy stupidity is loss.

Yes, it would make sense for all Democrats to approve both A and B. It is however quite probable that some voters will vote for their favourite only. This can happen because they do not understand that the secure strategy would be to approvo both. Or they can vote this way since they have a strategic incentive to make their favourite win instead of the other Democrat canididate.

> 
> From the point of view of overall social utility, this election could go to any of the three candidates and be approximately the same utility. Hence the method I'd want to see for this election is Score voting, if we must have a single poll. Bucklin would work fine, though. Bucklin allows voters to stand, for the early rounds of counting, for their favorite, while uniting before the election is over, if it's needed. The votes would presumably be
> 
> 26:A>B or A>.>B
> 26:B>A or B>.>A
> 24:C or C>.>A
> 24 C or C>.>B
> 
> (the period represents a blank rank. This was actually used in the Bucklin elections, it's clear. Some voters postponed compromising until the last rank.)
> 
> I'd say that Bucklin handles this election perfectly. A tie is unlikely, because voters will vary in how they add additional ranking. What determines how the voters actually vote is preference strength.
> 
>> 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?
> 
> It's obvious. Real voters will have little or no difficulty if they know the situation. There is no remedy for ignorance, though. I do have some question about designing voting systems to empower the ignorant. (By the way, that is *not* an elitist position, I'm ignorant, often, and systems that give equal weight to my ignorant opinion can make some poor decisions. Choice is another matter, but I won't go into that, beyond noting the important issue of consent to results, the reason why I strongly support systems that require majority consent for a result, directly or, if not directly, if that's not possible, then indirectly.)
> 
>> That situation is quite common, except that accurate ties in polls are not common.
> 
> The situation is extremely uncommon. Juho must be thinking of a three-party situation, and it is uncommon in three-party situations for the potential coalition to be equally divided as shown. The lesson: form coalitions and make coherent, united decisions. In the situation above, it looks like that is what the Republicans did. Are Republicans smarter than Democrats? Perhaps. If that's really the case, then they may very well be better at governing the society! Consider the election an intelligence test: be smarter, you will win, and society benefits from more intelligent governance.

I'm thinking about elections that have three potential winners (with any number of parties). There are not too many mappings of those three candidates to the political map. In this example two of them are quite near to each otehrs, and they have about equal "political distance" to the third candidates. Other settings might include e.g. a balanced triangle and three points on a "left-right" axis. If we have three potential winners, I claim that the set-up of this example is one of the common ones (if we allow some variation in the numbers but still maintain the relative positions of the candidates). What would be a more common political mapping of three potential winners?

> 
> There are much better methods possible for generating community intelligence, the factional division model is largely bankrupt. It worked to a degree, that's about all that can be said for it. It leads to really poor decisions, too often.
> 
>> 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.
> 
> The argument here leads to a conclusion that ranked Approval is better than unranked. Bucklin. But the difference is slight. Actual behavior of voters is not possible to predict from the model.

Bucklin collects some more information. The problem of Approval can be said to be the fact that the voters are not able to indicate the preference order of three candidates (but are forced to indicate equal support to two of them). Rankings and full ratings contain sufficient information for voters to indicate all their preferences.

> 
> The lesson: form coalitions and pursue a united strategy, ab initio. Improved voting systems are not a fix for failure to cooperate and collaborate.

Ok, works if parties are able to limit the number of credible canidates to two. But I have understood that the point of the planned reform is for many to be able to have more than two potential winners. So we must assume that we should be prepared also for the situation where there are three or more potential winners. In the given example the other "Democrat" could thus come from a party or grouping that is not under the control of the Democrat party, and whose nomination of a candidate can not be cancelled by the Democrats.

I thus accept limiting the number of candidates to two as one solution to the problem. But I guess the whole point of the reform is to allow more than two potential winners to take part in the election, and to be able to handle such situations.

> 
> The example does show the superiority of Bucklin over IRV. IRV, with naive voters, will award this election to C. Bucklin gives it to A or B without effort. Raw Approval could easily fail and likewise give the election to C. From the terms of the problem, none of the C voters will approva A or B, and all will approve of C. If *any* of the A and B voters fail to approve the other candidate, C could win.

What do you think about the Condorcet methods (that were discussed in this stream earlier) and their ability to cope in this kind of situatiions?

> 
> Approval *must* be seen as an improvement over Plurality, that's all. 

In many ways, yes. I think Approval has also some weak spots where it can fail also more dramatically than Plurality. Approval is good in the sense that it allows also additional minor candidates without them becoming spoilers (assuming that one wants that to happen). Its problem is that when the minor parties are no more minor but become potential winners, Approval voting strategies may become quite impossible to master, and the method becomes unstable (as in the example). For that reason I hope that an Approval based reform will continue and the method will be replaced with some better working method before the problmes three (or more) potential winners appear in real elections and cause people to turn their back to this method.

One question was not answered yet. How did the voters know that in this election they are supposed to approve both A and B? Is there a general strategy description that the voters could follow? Where is the border line where they should go back to approving only their favourite? The strategy can not be to always approve all the candidates of one's favourite wing. What if the numbers were 30, 30, 20, 20. Would that be a safe margin to allow A and B supporters to make a choice between A and B? Of course also with those numbers some of the voters would have to approve both A and B, or otherwise C wins. My general claim is that actually Approval is quite often clueless (and the voters are) as soon as this kind of situations with three or more potential winners appear. In this example the A and B supporters also have a strong strategic incentive to NOT approve the other candidate of the same wing. They may vote wrong and lose the election whichever way they vote.

Juho