[Election-Methods] Simple two candidate election

[Jan Kok]

Hi Rob,

I congratulate you for focusing on some questions that underlie the
endless debates about which is the "best", "fairest", etc. voting
method.

To restate the questions my own way: What do we _mean_ by "best",
"fairest", "most democratic", etc. Is there some standard (criterion,
figure of merit) that we can all agree upon for evaluating and
comparing voting methods?

It appears that, so far, there is no widely agreed-upon definition for
"best", fairest", "most democratic", etc. that can be used for
comparing voting methods. Nor is there some "gold standard" that we
can all agree upon for comparing methods. I had thought there were
only a couple commonly held standards, but I see from this thread that
there are perhaps four or more:

The Majority Criterion: roughly speaking, the majority of voters get their way.

Social Utility: pick the winner that maximally benefits society, or
gives maximal overall voter satisfaction, etc.

Equal voting power: all voters have equal influence over the election.

Minimize or eliminate the need or temptation for voters to vote strategically.

Some people (anarchists) reject the idea of voting entirely!

Many thousands of words have been written to try to define those
standards or criteria more precisely. I won't add to that verbiage
here. I think it's not very productive to haggle over detailed
definitions when we don't agree about which of those broad criteria is
"best".

Instead, I'll say a few words to promote my view that Social Utility /
Overall Voter Satisfaction / "Maximum Net Tangible Utility" (I like it
:-) is the "best" standard.

Preface: I don't think there is a way to "prove" that any of these
standards are "correct" or "best", using mathematical or philosophical
arguments. It seems to me that this is a discussion about personal
values - do you value social utility more, or do you value equal
voting power more? It seems almost axiomatic to me that Social Utility
is the "obvious" "best" standard. But I recognize that others may feel
the same way about the other standards. How can we move beyond such an
impasse? My approach to persuasion is to present voting scenarios
where I hope it will make sense to most readers that preference
strength should trump majority rule, equal voting power, etc. I am
also striving for some degree of realism, in the sense that people can
see how similar situations could occur in real elections. At the same
time I don't want the scenarios to be so realistic that some readers
will identify strongly with the majority and therefore conclude that
majority rule is best! (I'm explaining my strategy here because I want
to invite people to contribute more scenarios, in support of Social
Utility, or in support of the other criteria.)

Preface: Except for my initial infatuation with IRV, I have always
chosen my criteria first, and then chosen to support voting methods
that best satisfy those criteria. I have NOT chosen voting methods
first, then chosen criteria that justified my choice of voting method.

Ok, here are a couple of scenarios:

(Inspired by Clay Shentrup.) Consider an election where the choices are:
A. Spend $10 billion to find a cure for the common cold.
B. Spend $10 billion to find a cure for multiple sclerosis.
(Assume equal high probability of success for either choice.)
Presumably a lot more people suffer from colds than from MS, but MS is
devastating, while colds are generally just a nuisance. So, if voters
are selfish and shortsighted (and "honest" about expressing their
preferences), option A might win with a simple majority vote. But,
let's assume that option B gives better social utility. Wouldn't that
be the better outcome? A method such as fine-grained Range Voting,
which allows voters to express preference strength, would have a
better chance of making the "right" choice, if voters who are not
afflicted with MS and not worried about getting MS vote "honestly"
their weak preference for option A. On the other hand, if the A voters
strategically exaggerate their preference for A, then A would win.
That's no worse than the majority rule result.

Here's another, similar scenario. The choices are:
A. All people pay income tax in proportion to their income.
B. People whose last names begin with A through F pay twice as much as
they would in option A, and the rest pay $1 less than they would in
option A.
Assume the extra taxes collected in B are just wasted. So option B has
lower social utility, but the majority of voters - those whose last
names begin with G through Z - would slightly prefer option B. I
think/hope that most readers would agree that A is the "better" and
"fairer" choice. A simple majority vote would choose B. Range Voting
with honest voters is more likely to choose A. But if the G-Z voters
strategically exaggerate their preference for B, then the result is
the same as majority vote - no worse.

Would voters vote "honestly" with intermediate values, thus
voluntarily "weakening" their vote under Range Voting?

Warren D. Smith's 2004 exit poll study showed that a surprisingly high
fraction of the respondents (about 75% if I recall) voted with other
than max and min values. However, that poll had 6 candidates, so it
might not be a good indicator of what would happen in a 2-candidate
election.

I personally have voted on bylaws or platform issues at political
conventions, where I wanted to cast a weak vote rather than a strong
yes or no vote. The reason was that I had only a weak opinion, and
would have preferred to let those with strong opinions have their way
- but if nearly everyone had only weak opinions, then I might as well
register my opinion and participate in the decision.

Cheers,
- Jan