[EM] My Favorite Deterministic Condorcet Efficient Method: TACC

[Kathy Dopp]

> Date: Mon, 08 Nov 2010 23:58:43 +0000 (GMT)
> From: fsimmons at pcc.edu
>
> A few years ago Jobst invented Total Approval Chain Climbing or TACC for short.
>
> At the time I was too young (not yet sixty) to really appreciate how good it was.  It is a monotonic. clone
> free, Condorcet Efficinet method which always elects from the "Banks Set," a nice subset of the Smith
> Set (if not the entire Smith Set).
>
> It is easy to describe:
>
> (1) Initialize the variable S as the empty set  S = { }.
>
> (2)  While some alternative beats every member of S pairwise, augment the list S with the lowest
> approval alternative that does so.
>
> (3) Elect the last alternative added to S, i.e. the member of S with the greatest approval.
>
> That's it.
>
> Obviously the method will elect the CW when there is one.
>
> If the Smith set consists of a cycle of three alternatives, say A beats B beats C beats A,, then this
> method (TACC) will will elect either the member of this cycle with the greatest approval or the one with
> the second greatest approval, depending on whether or not the cyclic order goes up or down the approval
> list.
>
> What I didn't appreciate in my younger days was how beautifully resistant the method is to strategic
> manipulation.
>
> Scenario 1:
>
> 49 C
> 27 A>B
> 24 B  (sincere is B>A)
>
> The sincere CW is A, but the B faction creats an ABCA cycle by rruncation.
>
> Assuming that "approval" is the same as "ranked" in each of the factions, the approva order is (from
> greatest to least)  B, C, A .  Since this is in the same cyclic order as the cycle,  C wins.  If the B voters
> are rational, they will not truncate A!
>
> Now look at the burial temptation scenario:
>
> 49  A>B (sincere is A>C)
> 27  B>C
> 24  C>A
>
> The sincere CW is C.
>
> Now suppose that the A faction buries C as indicated above:
>
> TACC will elect B. whether or not the A faction approves B.
>
> Forest
>

I like it a lot Forest and believe it would make most voters happy
with the outcome. Great that it's monotonic and strategy resistant so
encourages sincere voting.

What does "clone free" mean again please?

It is a little tricky to count, not very intuitive, so I wonder how to
explain it so most people could understand its logic?  The logic seems
solid.

It is precinct-summable with an n x n matrix (n = # candidates) using
the diagonal for the # approval votes for each candidate.  Not sure
how to do the sampling mathematics for post-election audits - might be
a challenge to figure out how to limit the risk of certifying an
incorrect candidate.

Do you have a multi-winner version or a proportional representation version?

Regards,
-- 

Kathy Dopp
http://electionmathematics.org
Town of Colonie, NY 12304
"One of the best ways to keep any conversation civil is to support the
discussion with true facts."

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