[EM] TACC (total approval chain climbing) example

[Forest Simmons]

On Thu, Apr 24, 2014 at 5:15 AM, C.Benham <cbenham at adam.com.au> wrote:

>  Forest,
>
> Just because you can contrive some  example
>

Actually it was a range of examples. where the only requirement was that
the sincere Condorcet preference have the smallest first place support.


> where method X appears to resist Burial strategy better than method Y
> is no (or a very very weak) reason to suppose that one couldn't just as
> easily contrive a converse example (i.e. where method Y resists Burial
> strategy better than method X.)
>

I didn't claim that TACC was uniformly better with respect to burial.  I
only said that my examples showed that Woodall/Benham was not uniformly
better than TACC.



> This is especially the case without some sensible burial-resistance
> criterion that you can show is met by X or not Y, or failing that
> perhaps some computer simulation that shows that method Y rewards Burial
> strategists significantly more often than method X.
>
> Also, while you are comparing TACC with  Benham/Woodall and IRV I think
> should also be benchmarking it against the other two
> methods that combine pairwise and approval information,  Smith//Approval
> (almost the same thing as another method you promoted
> as "Majority Enhanced Approval", where you descend a chain starting with
> the most approved candidate, only adding candidates that
> covers all the already added candidates and then elect the last added
> candidate) and Schulze Approval Margins (the same thing, at least
> with 3 candidates, as Approval Margins Sort).
>

Yes, I was thinking that these other methods would require more thought
about where to put the approval cutoff, but your encouragement makes me
want to examine them again with respect to the Chicken Dilemma.  As you say
Smith//Approval is inadequate but I need to consider the approval margins
idea, and the descending covering idea, which has the advantage over TACC
of being Independent of Pareto Dominated Alternatives.

>
> Those other methods also deny the buriers in your example, without
> electing a candidate X that is both pairwise-beaten and positionally
> dominated by some candidate Y.  (Of course Smith//Approval  fails Chicken
> Dilemma, so we can leave that aside if you like.)
>
> An example that highlights TACC problems:
>
> 25 A>B  (sincere may be A or A>C)
> 06 A>C
> 32 B>C
> 27 C>A
> 10 C
>
> C>A>B>C,  Approvals C75 > A58 > B57  (Top Ratings  C37 > B32 > A31)
>
> TACC  rewards the A>B maybe buriers by electing A, even though C
> positionally dominates and pairwise beats A.   AM/AMS very comfortably
> elects C.
>
> If say, 2 of the 10 C voters change to B ( a Push-over strategy) then the
> TACC winner changes from A to C.
>

I'll look at this example later, but it may be moot now that I am starting
to look at approval margins, etc.

Thanks for your insights.

Forest

>
> Chris Benham
>
>
>
>
> On 4/24/2014 5:17 AM, Forest Simmons wrote:
>
> 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 and TACC elect C.
>
> Four years later the polls confirm that public opinion has not changed at
> all from the above ballot set, so candidate 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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