[EM] Quantifying manipulability

[Forest Simmons]

Let's try another example:

6000 A>>B>C
3000 C>B>>A
1000 B>C>>A

Let's say the above table represents the true distribution of preferences.

Obviously, A is the people's choice, while B and C are clones representing
the perceived interests of 40 percent of the voters.

Suppose that they are clones representing the true interests of the
wealthy corporations that control the popular media, pollsters, pundits,
etc, so that they have the means to propagate a misleading, intentionally
biased poll with the intent of manipulating the election.

Here are the published results of the false poll:

35% A>B>C
40% C>B>A
25% B>C>A

Candidate B is portrayed as a centrist candidate with poor first place
support, i.e. B and C are portrayed in the "good cop/bad cop" roles.

Let's put the true and false next to each other for comparison:

6000 A>>B>C   35% A>B>C
3000 C>B>>A   40% C>B>A
1000 B>C>>A   25% B>C>A

[This discrepancy is no big stretch for the corporate spinmeisters.]

Under Approval, candidate A would get exactly 60 percent approval.
Candidate B would get between 40 and 90 percent approval, depending on how
many of the 6000 voters of the A>>B>C persuasion were fooled by the poll
into reaching way down to support their "lesser evil" candidate B.

That would depend on the strength of their preferences of A over B.

Furthermore, as Mike says, they might be fooled once, but not a second
time.

Now for IRV:

Note that IRV, when played out in the fictitious poll result electorate,
would eliminate B first and give the win to C.

So believing in the poll, and applying rational strategy, the 6000 voters
of the A>>B>C persuasion (not knowing their real strength) conclude (one
by one while watching corporate sponsored public TV in the isolation of
their living rooms) that their first choice has no chance of winning, but
does have a good chance of spoiling their second choice's excellent chance
of winning against their last choice.

Therefore, they are sorely tempted to vote B>A>C.  Neither of the other
two factions has any incentive to vote insincere rankings, so if more than
half of the 6000 succumb to their temptation, A will be eliminated in the
first round, and B will win by a majority of transferred votes, an
artificial majority indeed.

The sad part is that they could easily be fooled a second time, since the
ballots don't show the strong 60 percent support for A.

How about Borda?  The fictitious poll results show B as the Borda
frontrunner and C as the runnerup.  The pressure for the first faction to
switch to B>A>C in order to reinforce B's expected win over C is a very
mild pressure, but if even 501 of the 6000 voters (less than one in ten)
of the A faction yield to this pressure, the win goes to B.

How about the various Condorcet methods? I'm no expert, but it seems to me
like the false poll exerts no incentive whatsoever for insincere order on
the ballots.  In particular, the 6000 can give full support of B over C
without having to move their favorite A downward in their ballot ranking.
So A wins hands down, whether or not the voters believe in the false poll.

How about Plurality?  I'll leave it to the reader to see that A's win is
not necessarily assured, depending on the level of belief in the poll and
the "rationality" of the voters' response to that belief.

How about Candidate Proxy?  Here, the voters are not too worried by the
polls because they know that their favorites' true levels of support will
become apparent when the proxy counts are in, and they trust the judgment
of their favorites in any case (which is basically why they are their
favorites).

Sure enough, when the Election Completion Convention convenes, candidates
A, B, and C are proxies for 6000, 3000, and 1000, voters respectively.
So under this method, candidate A's win is never in jeopardy.

In summary, IRV, Borda, Approval and Plurality, are susceptible to this
(the most dangerous) kind of manipulation, more so than Condorcet or
Candidate Proxy.

Approval acquires immunity after one bout. That's one reason why Approval
is such a good Election Completion Procedure for Candidate Proxy; the
proxy count serves as the inoculation that induces at least partial
immunity.

The other reason that Approval (or some other form of Cardinal Ratings
like Range Voting or Grade Voting) is ideally adapted to the Election
Completion Procedure is that the "reality check" feature of Candidate
Proxy (the requirement to post candidate rankings before the election and
vote consistent with them in the Completion Convention) makes it
imperative that the Election Completion Procedure obey the Favorite
Betrayal Criterion (FBC).

If the Procedure did not obey that criterion, then optimal strategy would
not always be consistent with the pre-election posted rankings. The
proxies could not vote in accordance with their best judgment, and so the
voters could have reason (in some cases) to choose as proxy someone with
lesser judgment but in a better position to influence the outcome (given
the artificial constraints).

In other words, if the Election Completion Procedure does not satisfy (or
nearly satisfy) the FBC, then the "reality check" feature is a benefit
that comes with a cost, in some cases a cost that is not balanced by the
benefit.

For example, if the Election Completion Procedure were Plurality, the
reality check would make the Candidate Proxy method strategically
equivalent to Plurality itself, canceling out any possible benefit.

On the other hand, without the reality check, Candidate Proxy with
Plurality as the Election Completion Procedure would be a definite
improvement on most other methods including Plurality, IRV, and Borda, as
the above example shows.

But the win-win combination is having Approval as the Election Completion
Procedure while keeping the reality check.


Now, how about some more examples of the above type of manipulability?

Forest

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