[EM] TACC (total approval chain climbing) example

[C.Benham]

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

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20140424/6c1c0458/attachment-0005.htm>