[EM] My Favorite Deterministic Condorcet Efficient Method: TACC

[fsimmons at pcc.edu]

> Chris wrote ...
> 
> >/ 31: A>B
> />/ 32: B>C
> />/ 37: C>A
> />/
> />/ Approvals: B63, A68, C69. A>B>C>A.
> />/
> />/ TACC elects A, but C is positionally the dominant candidate and
> />/ pairwise beats A.
> />/
> />/ For a Condorcet method with pretension to mathematical elegance,
> />/ I don't/ /see how that/ /can be justified.
> />/
> />/ Chris Benham
> />/
> />/ PS: Could someone please refresh our memories: What is the
> />/ "Banks Set"?
> /
> Forest Replies:
> 
> 
> >As you know C is the DMC winner, and would be a slightly better 
> winner, given
> >that the ballots are sincere. But DMC is not as burial 
> resistant and truncation
> >resistant as TACC. 
> >
> >It is interesting that DMC and TACC have opposite rules for 
> which of the top two
> >approval members of the top cycle (of three) wins. DMC awards 
> the win to the
> >one (of these two) that beats the other. TACC awards the win 
> to the one that is
> >beaten by the other.
> 
> 
> Chris: 
> I have long since abandoned the "Definite Majority Choice" 
> (DMC) method in
> favour of Smith//Approval (as my preferred Condorcet method), 
> which also elects C 
> here.
> 
> I still like the Definite Majority criterion, which says that no 
> candidate that is
> pairwise beaten by a more approved candidate is allowed to win.
> 
> I think that (in isolation) meeting the Condorcet criterion is 
> desirable, but not so
> holy that on discovering there is no voted CW the method should 
> proceed on the assumption
> that there is really a "sincere CW" that has been victimised by 
> strategists the method
> should try to frustrate or punish.
> 
> Condorcet methods are vulnerable to Burial, period. Futile 
> attempts to address this
> should not be at the expense of producing winners that can have 
> no philosophical
> justification on the assumption that all the votes are sincere 
> (or are all equally
> likely to be sincere).
> 
> The TACC winner A simply has no shred of justification versus 
> the Smith//Approval
> winner C.
> 
> Forest:
> 
> >I've come around to the belief that most Condorcet cycles in 
> ordinary elections
> >are artificial, so chances are that this cycle was created from 
> the burial of B
> >by the C faction. Giving C the win only rewards this manipulation.
> 
> 
> Chris:
> I can't see any remotely rational justification for assuming 
> that this is the case
> rather than, say, the cycle was created by the A voters burying C.
> 

Well, usually the largest faction is the one with the best chance of getting away with it, and would get 
away with it under Beatpath, Ranked pairs, etc. unless the Condorcet supporters took defensive action.  
With TACC no defensive action was necessary.

Now let's consider the possibility that you suggest, namel;y that the true preferences were

31 A>C
32 B>C
37 C>A

If there is enough information for the A faction to think it is safe to bury C, then there is enough 
information for the C faction to take the precaution of truncating A defensively.

The we have

31 A>B
32 B>C
37 C

That's why I think this scenario is less likely than the one i suggested.

To continue this scenario, we see that A now has the leasrt approval.

Under TACC, as long as the cyclic order of the cycle is A beats B beats C beats A,, and A has the least 
approval of these three alternatives, C will win.  In other words the defensive action saves the day for the 
sincere CW.

In this case the burial doesn't backfire on the defecting faction, but it doesn't do any good either.  

Forest