[Election-Methods] RE : Corrected "strategy in Condorcet" section

[Abd ul-Rahman Lomax]

At 03:22 AM 8/18/2007, Juho wrote:
>I forgot to mention this special case that doesn't touch the main
>theme of this mail stream but is maybe worth noting anyway.
>
>An example with two parties, ABC and DEF. The voters have zero
>information. But the strategy of the DEF party pays off and they will
>win. Not an easy strategy to implement but it sometimes works.
>
>30 A=B=C>D=E=F
>10 D=E=F>A>B>C
>10 D=E=F>B>C>A
>10 D=E=F>C>A>B

What interests me is that the effective of strategic voting is being 
studied with a case showing, for some method or other, a success. The 
presumption in this scenario is that the rankings are not sincere, 
they are merely a device for winning in a situation where there is a 
tie. But it's zero knowledge. The DEF party does not know that it is 
going to be a tie. They don't even know if it is close.

Now, if the votes are sincere, we can still look at this scenario and 
consider whether or not the result is reasonable. Is it? I'm not sure 
of the method being studied, I haven't been following the discussion, 
but I suspect that some methods would assume that the defeats created 
by the DEF party indicate something about the desirability of a DEF 
candidate over an ABC candidate, when clearly the actual situation is 
that there is no real cause fo this. I've never studied the various 
Condorcet resolution methods.

Further, I look at this and notice that the ABC party is claiming to 
be totally indifferent as to the pairwise elections between D, E, and 
F. Odd, don't you think? Similarly, the statement that the voting 
pattern of the DEF party is a strategy, difficult to pull off, but 
that "sometimes works," implies that the DEF party "sincerely" has no 
preference between the ABC candidates.

Given that, I suspect, we have never seen this pattern appear in an 
election, what would really be correct is that "sometimes it *could* 
work. However, wouldn't it be relevant to ask, if this is zero 
information, which is more likely: that it would work, or that it 
would result in a worse election outcome, for most of the strategic 
voters, than if they voted sincerely?

Here, what has been developed, I assume, is a piece of evidence that 
it can be strategically advantageous, with these methods, to 
distribute a coherent party vote as, instead, of equalities, split 
preferences that cancel each other out. I assume that this is because 
the method is making an assumption about the meaning of defeats and 
"defeat strengths," a quite dicey proposition with a method that does 
not measure preference strength.

There is no risk to the strategy described *if the DEF voters 
actually have no significant preference between the ABC candidates.* 
In that case, they are merely tailoring the exact pattern of their 
voting to what is most effective in the system.

What is a preference? Often in these discussions, we consider that it 
is obvious. However, the term must be understood as a member of a 
pair of opposites, in a sense. There is a preference or there is no 
preference. Here, there is an assumption that there is no preference. 
However, it is asserted here that there is an advantage to voting a 
preference, under some conditions, when there is not. Does this not 
create a preference? Only if we assume that preferences exist in the 
abstract, entirely aside from the context of the election, and the 
election is merely collecting these ideally undistorted preferences 
to determine the result, would we be able to say that, no, it does 
not. We could then assert that preference has nothing to do with the 
election process; I would prefer A to B no matter what election 
method is involved.

But we routinely disregard the effect of so-called "irrelevant 
alternatives." Sure, I may prefer A to B, but that preference may so 
greatly pale in comparison to my preference for another candidate, C, 
that I cannot, in conscience, cast any vote that would improve the 
chances that  A or B would defeat C.

In Approval, this is simple: I vote for C and thus effectively equate 
A and B at bottom rank. Likewise in a ranked method, I'd do this if 
allowed. Since I have a preference between A and B, and in a method 
that allows more than the binary ranking of Approval, some would 
claim that my vote is strategic if I rank them equally.

In a ranked method, though, if I'm forced to rank all candidates on 
pain of having my ballot thrown out, then I would translate C>A=B to 
one of the two remaining rankings, say C>A>B. What is offensive about 
this vote is that it creates an equality between the preference 
strength of the C>B pair with that of the A>B pair, which is 
drastically not the case.

Even though I have a preference between A and B, C>A=B is a more 
accurate expression of my sincere opinion than C>A>B or C>B>A.

The whole concept of strategic voting is problematic. Some methods do 
reward clear distortion of preference, i.e., preference reversal, 
which is intuitively offensive. However, converting a supposed 
equality into a preference is trivial. It was said that it was 
difficult to pull it off.

But if we take as an additional condition that the DEF voters have no 
preference at all between the ABC candidates, which was implied, it 
would actually be quite easy. The DEF party would simply provide a 
reward for voting according to a certain patter. The reward would not 
be personal to the voters, for that would be unlawful, but it would 
be some lawful public action that the voters would wish to see take 
place. According to voter registration in precincts, as one example, 
the DEF party could allocate funding for local DEF party activities, 
if the DEF vote in those precincts were according to a certain 
pattern, say D=E=F>A>B>C. Compliance would, of course, be voluntary, 
but we are already assuming a party that votes totally coherently 
(and the same exists on the other side). Suddenly there is a small 
preference created for the preference pattern indicated, these voters 
actually would prefer to see A elected more than B more than C. So if 
they vote that way they are voting sincerely.

I am, to some extent, deconstructing the concept of voting preference 
as it is often used to describe the behavior of methods. This really 
becomes important, politically, when we come to the study of 
so-called "strategic voting" in Range, where it is common to assert 
contradictory conditions in an election scenario, and then claim some 
benefit for "strategic voting."

If I have no preference between A and B, and a party with which I am 
affiliated declares that A is preferable to B, for party purposes, 
and depending on my relationship with and trust in that party, I may 
well now have a preference. Conversely, if I have a preference, and 
the party declares that giving any of a set of candidates a vote of 
any strength at all is harmful, I may equal rate these candidates bottom.

*And it would be sincere.*

What is commonly done is to assert that there is really a preference, 
but the "strategic voter" bullet votes, concealing the preference, 
and, it is asserted, can thereby gain an advantage. Usually it is 
neglected that such votes are actually hazardous; while the voter 
might gain some advantage, in other situations the voter can lose 
value in the result by concealing preference. It appears that, 
generally, a sincere vote in Range, properly defined, is as good as a 
so-called strategic vote, overall, in a zero-knowledge election.

And that bullet voting can be powerful is most obvious if we look at 
a full knowledge choice made by a voter. The voter either knows that 
the voter's vote is moot, that it cannot change the outcome, or the 
voter knows that the voter may create or break a tie, and sometimes 
more than one tie, so it is totally ordinary that the voter would 
vote to maximize personal utility, which, in this case, will have 
negligible effect on overall utility, since, without this voter's 
vote we were either at or within one vote of a tie.

We *want* voters to vote to maximize their personal expected outcome. 
If a voter thinks that outcome will be maximized by voting a certain 
way in Range, that is actually how the voter should vote! However, 
with zero knowledge, there are powerful reasons for voting 
intermediate preferences, and, even with full knowledge, there would 
be reasons for voting such middle preferences, as long as it did not 
impact the outcome negatively for the voter. For example, if the real 
pairwise election is between A and B, and I have a preference, I will 
bullet vote within that pair, but I can vote however I like with 
regard to all other candidates, there is no reason *not* to give 
intermediate ratings. They are moot for determining the winner, but 
they may help my personal cause politically.