[EM] My Favorite Deterministic Condorcet Efficient Method: TACC

[Jameson Quinn]

2010/11/8 <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.
>

But if the A faction votes A>B>C (ie, if they approve C), then C wins. So I
think that this method would work best with only 3 rating levels (only 2
approval levels) available.

>
> Forest
>
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