[EM] "Strategy-Vulnerability"

[Michael Ossipoff]

"This sheds light on a question someone else posed: Why aren't better
voting methods actually used in small organizations?"

Approval, Score, Beatpath, MinMax(wv), Borda, IRV, Plurality, and
probably a number of other voting systems are used in small
organizations.

No matter which of those methods someone considers "better", there are
small organizations (and large ones too, like the U.N.) using it.

"The choice of which method is 'best' is not obvious."

...But the problem occurs when some advocates and promoters _think_
that it's obvious.

"And when voting is done by
people who understand how to vote strategically, the strategy-vulnerable
methods..."

This confusion about "strategy-vulnerable" is popularly-repeated.
Strategy is an attribute of all non-probabilistic, non-dictatorial
voting systems.

The word "vulnerability" implies that the strategic voter is doing
some wrong against the voting system, or corrupting its pureness and
rightness.

No, every voting system simply calls for non-sincere voting, as one's
optimal way to vote. That isn't good or bad, it's just a fact of life,
for voting systems. And voting strategically, voting in one's best
interest, voting optimally--that isn't bad or devious either.

There's one instance in which the expression "strategy-vulnerable"
could legitimately mean something. For example, I I described how, in
AOCBucklin, the C voters could cause a chicken dilemma among the {A,B}
voters. That can meaningfully and fairly be called a vulnerability.
That usage makes some sense when we're speaking of how an
offensively-intended strategy could cause strategy problems or
dilemmas for others.

But that isn't the case in Score, the method to which this poster was
referring.   ...or in Approval either.

All voting systems are "strategy-vulnerable", in the sense that that
poster means that usage. That includes all rank methods. It includes
all Condorcet methods, including Beatpath and Kemeny.

In our u/a elections, for the most part, the best that a rank method
can do is duplicate the strategy of Approval or Score. (Except that
some rank methods can actually improve a little on Approval, by
getting rid of the chicken dilemma).

In the traditional unimproved Condorcet methods, such as Beatpath and
Kemeny, general u/a strategy is unknown. But, in the simple
not-so-general situation that exists in this country, their strategy
is known, and simple. Voters believe, having always heard it from
media, 1) that the corrupt Democrats are acceptable; and 2) that the
winner will always be a Democrat or a Republican. Republicans are
regarded as unacceptable by those who prefer Democrats to them.

The optimal u/a strategy, given those beliefs, is simple and
uncontrovesial, in traditional unimproved Condorcet: Rank the Democrat
alone in 1st place.

That's strategy, you know. So guess what: Traditional unimproved
Condorcet methods, such as Beatpath and Kemeny, are "vulnerable to
strategy" (if you use that term to mean "possessing strategy".

So how do "strategy-vulnerable" methods differ from eachother? By the
undesirability of their strategies. By the amount by which their
strategies distort voters' preferences. For instance, Beatpath and
Kemeny's optimal strategy under the above-specified conditions,
involves favorite-burial. That isn't true of all voting systems. For
example, it isn' true of Approval or Score.

" -- in this case score-ballot-based counting -- easily produce
unrepresentative results."

You mean like the results when people vote an unliked compromise over
everyone they like better, as described above?

Or do you mean like when, in Approval, people use their optimal
strategy of approving all of the acceptable candidates (in a u/a
election), or all of the above-mean candidates (in a 0-info, non-u/a
election), or all of the better-than-expectation candidates (in a
non-u/a, non-0-info election), thereby electing the candidate
acceptable to the people, or the candidate regarded by the most people
as better than average, or the candidate who is, for the most voters,
better than what they expected of the election?

You mean unrepresentative like that?  :-)

In Score, the optimal strategy is to vote as in Approval, thereby
giving Score the same strategy attributes as Approval.

Score differs from Approval in its built in, easier, fractional
ratings. Fractional ratings are useful for the
strategic-fractional-ratings for dealing with the chicken dilemma, and
when the voter is in doubt about whether a candidate should get a max
or a min rating. Also, Score's greater expressiveness seems to work
better with the way that many people are inclined to vote.

Approval can do fractional ratings too, but probabilistically.
Approval's much greater simplicity of count, and inexpensive
implementation, and minimal change from Pluralitly, and elegant
simplicity probably make Approval a more feasibly enactable proposal
than Score. Also, its simple count brings some practical advantages.

Mike Ossipoff