[EM] TACC (total approval chain climbing) example

[Forest Simmons]

On 04/21/2014 11:39 PM, C.Benham wrote:
>
>> Forest,
>>
>>  48 C
>>> 27 A>B
>>> 25 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.
>>>
>>
>> Benham and Woodall are a lot more resistant  to Burial than TACC (and
>> other Condorcet methods that meet mono-raise, aka monotonicity) because
>> they meet
>> "Unburiable Mutual Dominant Third"
>>
>
How about the following set of sincere preferences?

40 A>C>B
35 B>C>A
25 C>A>B

Candidate C is the sincere winner under Benham, Woodall, TACC, or any other
method meeting the Condorcet Criterion.

Suppose that the A faction decides to bury C:

40 A>B>C
35 B>C>A
25 C>A>B

Woodall, Benham, Condorcet (both wv and margins) reward this subterfuge by
electing A, whereas under TACC  the tactic backfires by getting B elected.

Under Condorcet (wv) the C faction can defend itself by truncating to 25
C.  This wouldn't help under Woodall/Benham:

You get the same result if you replace the respective faction sizes 40, 35,
25 with any three positive numbers a, b, c that satisfy both a>b>c and
b+c>a.

Now consider the following example where b>a>c:

35 A>B>C (sincere A>C>B)
40 B>C>A
25 C>A>B

Woodall/Benham still rewards the burial.  TACC elects C without any
defensive move.  Condorcet elects B without any defensive move.

Under TACC or Condorcet it never hurts and sometimes helps for the CW
supporters to truncate the rest of the candidates. But as you can see in
the cases we are dealing with here, only much more drastic defensive action
can save the CW under Woodall/Benham.

Conclusion: although in some cases the UMDT confers a superior defense
against burial, that doesn't make Woodall and Benham uniformly more burial
resistant than TACC.

Forest
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