[EM] To Condorcetists:

[Abd ul-Rahman Lomax]

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.

>[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.

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

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.

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?

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.

 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.

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.

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

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.

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