[EM] Majority Criterion, hidden contradictions

[Michael Poole]

Abd ul-Rahman Lomax writes:

> At 08:01 AM 11/2/2006, Michael Poole wrote:
>>The Majority Criterion is an objective criterion.
>
> It looks that way. When you look closer, there are some ragged
> edges. What does "prefer" mean? Is there a threshold in preference
> strength below which it is effectively the same "rating." I.e., the
> voter might make a choice, if forced to by the method, but really has
> no *significant* preference.

Wikipedia:

  By the majority criterion, a candidate X should win if a majority of
  voters answers affirmatively to the question 'Do you prefer X to
  every other candidate?'.

A voter who cannot honestly or easily answer "yes" to some candidate
is not a problem for this formulation of the majority criterion.  The
existence of such a voter is an argument in favor of some other
criterion, but does not make the MC subjective.  If you want to change
the "prefer" to "strongly prefer", pick a new name for your modified
criterion.

> Further, it is alleged that Approval does not satisfy the Majority
> Criterion. It seems to me that this requires a few assumptions that
> have not been made explicit.

It does not require any additional assumptions.  Approval can only
capture preferences between members of the approved set and the
not-approved set.  Clones are a good general example.  With small
numbers of voters -- for example, one -- Approval can result in ties
if the voters mark who they approve (or strongly approve) of rather
than who their favorite.

>>   When you ask about
>>preference strength, it becomes extremely subjective -- and attempts
>>to normalize the subjective effects (for example, rescaling each
>>voter's expressed preferences to a common minimum and maximum) obscure
>>honestly expressed preferences.  While one can reasonably complain
>>that objectively defined measures to not maximize subjective goals,
>>the superiority of the subjective measure should be established[1]
>>first.
>
> Doublespeak, I'd say. It is quite clear that there is some basis for
> variation in preference strength. It's real. It is no more subjective
> than preference itself; simple preference has taken the complex space
> of voter expectation and has reduced it to a binary relation. A lot of
> data is lost.
> 
> Is that data of value? I've shown situations where it clearly is of
> value, where the Majority Criterion will clearly choose a winner who
> will be a disaster for the society. And historical examples can be
> shown.

That data is not of value because my question was not "Is there some
reason for the variation in preference strength?".  The argument
advanced in favor of Range Voting is that it maximizes a certain
social utility function.  Exactly *which* function depends on whether
a ballot scores are normalized.  My question is why that particular
function is an appropriate optimization goal.

I suspect that the expected time to choose a disastrous winner is
lower for Range Voting than for methods that satisfy the Majority
Criterion.  True or not, comparing actual past performance to
hypothetical future performance is not a reasonable way to judge.

>>Ultimately, social utility is not a static function[2]; election
>>results alter the function both directly and indirectly.
>
> Yes, of course. But the very idea of elections is to derive some kind
> of conclusion from the state of the voters at the time of the
> election. This very idea is defective, that is, not optimal, but once
> we accept it, that further expectations will change after the election
> is irrelevant. The election is attempting to determine "the choice of
> the electorate." And we are attempting to define what that means.
>
> Essentially, how is the choice made, and for what purposes and to what
> ends. If we don't consider the ends, but merely consider a very
> limited metric, on the argument that this metric is "objective," even
> though it is entirely based on subjective comparisons by all the
> voters, we end up with an artificially constrained result that will be
> distorted, under some conditions -- I would argue that it is commonly
> so -- away from optimum.

The impact of an optimization goal on future system behavior should
not be dismissed so lightly.  You can balance on a unicycle, but you
seldom have to worry about balance in a sedan.

When there are only two viable parties, Range Voting's use of strength
of preference apparently encourages the factions to be strongly (even
bitterly) divided: that will maximize the difference in scores between
the two candidates among supporters of each party.  I am not sure that
more parties will necessarily resolve that; as Kevin Venzke showed, a
voter is most likely to affect a Range Voting election by giving only
extreme ratings.

The only non-personal justification I could find in the rest of your
email for a Range or Approval style vote is the pizza example.  I am
less interested in contrived examples -- I could contrive some
involving an irrational fear of pepperoni -- than in a formal
definition of Range Voting's social utility function.

Michael Poole