[EM] My Favorite Deterministic Condorcet Efficient Method: TACC

[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