[EM] TACC (total approval chain climbing) example

[Forest Simmons]

Chris,

What you say below makes perfect sense in a zero information election.

Now suppose the actual ballot set is

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

Then IRV elects A while Woodall/Benham abd TACC elect C.

Four years later the polls confirm that public opinion has not changed at
all from the above ballot set, so candidatee A convinces her supporters to
bury C. The ballot set becomes

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

Neither IRV nor TACC is affected by this burial, but Benham&Woodall reward
the A faction for their strategic order reversal.

It appears that IRV (in general) and TACC (at least in this case) are less
vulnerable to burial strategy than Benham/Woodall.

But let's take this case a little further.  Since the B supporters prefer
C over A, they have a strong incentive to protect C from this obvious
threat.  What can they do under IRV or Benham/Woodall?  They can betray
their favorite B and vote 40 C>B, which does get C re-elected, thus
rewarding their order reversal.

Forest

On Wed, Apr 23, 2014 at 7:44 AM, C.Benham <cbenham at adam.com.au> wrote:

>  Forest,
>
>
>  40 A>B>C
> 35 B>C>A
> 25 C>A>B
>
>
> In this example ballot set of yours (which you say is the result of the A
> faction burying against the sincere Condorcet Winner C) there is no reason
> to suppose that any of the ballots are more likely to be insincere than
> any of the others.
>
> In this sort of situation (with 3 candidates in a cycle and all the
> ballots containing the same amount of information) we should avoid electing
> a candidate
> X that is positionally dominated, especially by a candidate that pairwise
> beats X.   In this case that just says "not C".
>
>  35 A>B>C
>  40 B>C>A
> 25 C>A>B
>
>
> In this ballot set (which again you say is the result of the A faction
> burying against C)  TACC elects C.  But again there isn't any information
> on the ballots
> that suggests that some ballots are more likely to be insincere than any
> others.
>
> So the result must be justifiable on the assumption that all the votes are
> sincere. On these ballots C is positionally dominated and pairwise beaten
> by B.
> B also positionally dominates A.
>
> Approval Margins, Approval Margins Sort, IRV, Benham, Woodall and all
> other good  (and/or sane) methods elect B.
>
> Chris Benham
>
>
>
>
>
> On 4/23/2014 7:29 AM, Forest Simmons wrote:
>
>
>
>
>
>  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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