[EM] majority criterion

[Warren Smith]

>robla:
I've seen a lot of different definitions of the "majority criterion",
but for purposes of this email, I'll describe a minimal version:
"If a strict majority of the voters rank a particular alternative as
their unique first choice, then the voting method must select that
alternative as a unique winner" (Anderson, 1994)

--this criterion is not a desirable criterion for a voting system to obey.

An example is this.  51% of voters prefer that slavery exist but their
preference is mild.  (If slavery exists, they get to buy shooes for a cheaper
price.)   49% of voters are going to become slaves & spend the rest of their lives
in handcuffs, if slavery is enacted, and hence vote against it.
It is not desirable that the 51% win this vote.   Range voting will not
necessarily cause the 51% to lose the vote (they will still win if
all voters are strategic)  but it at least leaves the possibility open.
Therefore, by robla's very onwn example, but interpreted correctly this time,
range voting is clearly superior to all the other systems he mentioned.


I suggest concentrating on criteria which are actually important for
voting systems to obey.  Those are criteria which lead to greater social good
coming about.  There is a scientific way to measure that. It is
called Bayesian regret.   Measurement of the Bayesian regret of different
voting systems have been made.  Range is the current winner among those
systems for which the comparative measurement has been made.

Also, another way to distinguish voting system criteria that are important, from
ones that are not, is the situations that come up MORE OFTEN, and which when they
arise cause MORE HARM, are the ones to worry about.  So for example, range voting
failing to elect a majority winner, is somethign that will not happen often,
so we see this is not an important criterion.   However, the failure of DH3
(see http://math.temple.edu/~wds/crv/DH3.html)  is a very common and very serious
failure of every Condorcet method.  You have to weigh the relative importances
of different property failure by weighing their relative commonness and their
relative seriousness judged by the quality-dcrease in the election result you get.
Robla, were he to do that weighing, would conclude that the DH3 pathology
suffered by all Condorcet methods, is a more serious problem than the majority
winner criterion (rarely) suffered by range (and when if does happen, it is
probably not leading to a way-lesser-quality winner).

For example: I suggest to you, that had all previous US presidential elections been done
with range, then in not a single instance would the range winner have differed from the Condorcet
(honest votes) winner.   This suggests to me robla's concerns are focusing on
a rare problem.  I suggst focusing on a common problem.

In practice I find it very unlikely that range will disobey the majority criterion.
But in the event it ever does, that is quite probably a good thing.

-Warren D. Smith