[EM] Majority Criterion, hidden contradictions

[Michael Poole]

Abd ul-Rahman Lomax writes:

> I've been realizing just how defective the Majority Criterion is. 
> People tend to assume that the Majority Criterion is an important 
> characteristic of any proper democratic election system. Yet the 
> Criterion itself suffers from a number of serious problems.
>
> (1) It is clear that any method which satisfies the Majority 
> Criterion cannot maximize the expected value of the election. Range 
> is the method which directly does the latter, and this is directly 
> connected with its non-satisfaction of the Majority Criterion.

The Majority Criterion is an objective criterion.  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.

Ultimately, social utility is not a static function[2]; election
results alter the function both directly and indirectly.  Given the
upset caused by the last two US elections, this feedback is perhaps a
factor in your argument that an election should maximize social
utility.  However, I suspect negative feedback makes the system
unstable by encouraging radicalization by opposing factions.  An
unstable objective makes it more important to explain why that
objective should be sought.

[1]- Any proposal to maximize social utility that is to be taken
seriously in the US should avoid arguments that could be rephrased or
paraphrased as seeking "the greatest good for the greatest number" --
those are too easily comparable to communism, which had its own
failures due to preference for subjective over objective measures.

[2]- Suppose that 5% of the populace have no preference between two
major candidates, 50% have a slight preference for one, 40% have a
slight preference for the other, and 5% have an irrationally strong
preference for the second.  Include distasteful-to-somebody third
parties as needed for rescaled ballots to reflect honest preferences.
If the irrational strength of preference by 5% of people outweighs the
slight opposite preference by 10% of the population, it seems more
likely to push some of the 50% group to their own irrational extreme.

Michael Poole