[EM] TACC (total approval chain climbing) example

Forest Simmons fsimmons at pcc.edu
Sat Apr 19 16:28:20 PDT 2014

Let's consider the following ballot set:

48 C
27 A>B
25 B

Plurality says that A cannot win, because C has more top votes than A is

The Chicken Dilemma Criterion says that B cannot win, because there is a
possibility that the B faction is defecting from a true preference of B>A.

That leaves C as the only acceptable winner for this ballot set.

How do various methods stack up on this ballot set?

MinMaxPairwiseOpposition (MMPO) elects A.

Condorcet(wv) and Condorcet(margins) both elect B.

Implicit Approval elects B.

Borda, TACC, and IRV based methods like Woodall and Benham elect C.

But Borda is clone dependent, and the IRV style elimination based methods
fail monotonicity.  So TACC is a leading contender if we really take the
Chicken Dilemma seriously.

But what if the ballot set is sincere?

In that case it seems like B should be the winner.

The problem is that standard election methods have no way of detecting
ballot sincerity.

Therefore there is no strategy free method for covering both scenarios.

The question now becomes which requires more drastic strategy?

Note that if the above ballot set represents sincere preferences, the A
faction can help elect B by voting A=B, which requires no order reversal.

This move will work in any of the above mentioned methods!

Now suppose that the true preferences were

48 C>B
27 A>B
25 B>C

Then B is the Condorcet Winner.

But under both Condorcet wv and margins, there is a burial incentive for
the C>B faction to change votes to 48 C>A .  If B takes no defensive
action, this burial strategy will succeed.

Under TACC that burial strategy will backfire by electing electing A.

However, if the C>B faction may still be tempted to take the a more sincere
approach of merely truncating B.  When the B faction responds to this
threat by truncating C, we are led back to the original ballot set given

48 C
27 A>B
25 B

Which must have C as the winner if we want to honor Plurality and CD.

But then the A>B faction has a strong incentive to raise B to 27 A=B.

This solves the problem without any order reversals.

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