[EM] (3) MJ -- The easiest method to 'tolerate'

[C.Benham]

On 9/7/2016 10:15 PM, Jameson Quinn wrote:

> C: C is the clearly voted Condorcet winner
>
> But not the majority Condorcet winner. I regard majority Condorcet as 
> something any good voting system should tend to respect, but 
> non-majority Condorcet as only a weak signal.
>

C: The Majority Condorcet winner is always the Condorcet winner. It is 
ridiculous to suggest that failing to elect a Condorcet winner is a step 
in the
direction of  "tending to respect the majority Condorcet winner".

The "Majority Condorcet" concept is vulnerable to Irrelevant Ballots, 
and to put it forward as some especially desirable criterion is 
nonsensical.

In our example, would removing 3 plumping ballots from each of the 
candidates really turn C into a stronger candidate?  Because the effect 
would
be to change C from a mere Condorcet winner (who you say should lose to 
the approval winner) into a fabulous  Majority Condorcet winner (who you
say the method should "tend" to respect).

(The only point of the criterion is that some methods happen to be able 
to meet it, but not the normal Condorcet criterion.)

20: A>B
25: B>A
20: C>B
26: C

91 ballots.  Majority threshold = 46.

C > B  46-45,    C > A 46-45.

Or of course the question can be posed the other way: does giving each 
candidate 3 extra plumping ballots really make C a weaker candidate?

> Whoops... I'm sorry. Those were the averages over a large number of 
> polls, but then a week before the election, A had a heart attack. The 
> actual scores, with 3 ballots still to count from A's former 
> stronghold precinct, are:
>
> 48: B
> 49: C
>
> I guess C wasn't so dominant in top-ratings after all. Once we count 
> those last three ballots, we'll have a clear winner here, and there's 
> every chance it could be B.

C:I take it this is Jameson not being serious (and perhaps trying to 
shift goal-posts).

One of  IBIFA's obvious advantages over  "U/P" and MJ and the other 
Bucklin methods is that it has a
much weaker truncation incentive.  In the example (with 100 ballots)  
U/P penalised the 20 C>B voters
for not truncating. Had they done so C would have won. (Unsurprising, 
since that would have made C positionally
dominant as well the Condorcet winner).

It seems that you want a quite complicated method with a nearly as 
strong as possible truncation incentive and that nearly always
simply elects the Approval winner (while somehow "tending to respect" 
majority Condorcet without actually meeting the Majority
Condorcet criterion).

BTW, I'd be mildly interested in seeing one or two of your realistic 
examples where U/P doesn't elect the Approval winner.

Given from what I can make of your method goals, why don't you simply 
propose  Majority Condorcet//Approval ?

Chris Benham

>
>
> 2016-09-07 8:17 GMT-04:00 C.Benham <cbenham at adam.com.au 
> <mailto:cbenham at adam.com.au>>:
>
>
>     3: A
>     20: A>B
>     25: B>A
>     3: B
>     20: C>B
>     29: C
>
>     C > B  49-48,   C > A 49-48,   B > A 48-23.
>
>     Top Ratings scores:   C 49,   B 28,   A 23
>
>     Approval scores:      B 68,   C 49,   A 48.
>
>     On 9/7/2016 7:09 AM, Jameson Quinn wrote:
>>     IBIFA elects C. U/P elects B. It's clear to me that B is better.
>>     The 3 A-only voters are likely attempting a chicken strategy.
>
>     C: C is the clearly voted Condorcet winner
>
>
> But not the majority Condorcet winner. I regard majority Condorcet as 
> something any good voting system should tend to respect, but 
> non-majority Condorcet as only a weak signal.
>
>     and by far the most top-rated candidate.
>
>
> Whoops... I'm sorry. Those were the averages over a large number of 
> polls, but then a week before the election, A had a heart attack. The 
> actual scores, with 3 ballots still to count from A's former 
> stronghold precinct, are:
>
> 48: B
> 49: C
>
> I guess C wasn't so dominant in top-ratings after all. Once we count 
> those last three ballots, we'll have a clear winner here, and there's 
> every chance it could be B.
>
>     The suggestion that "B is better" because of
>     some guess that 3 truncators are "likely" attempting some strategy
>     is absurd.
>
>
> No, B is better because B has majority approval where C is rejected by 
> a majority. The argument about likely truncation is merely how IBIFA 
> went wrong, not how U/P got it right.
> ...Again, I don't regard this as a knockdown argument against IBIFA. 
> It's only one scenario; a roughly plausible one, but not particularly 
> likely. I think we should probably drop this. But I do think it 
> demonstrates pretty conclusively that IBIFA at least isn't strictly 
> dominant. After all, as long as we're making up arbitrary scenarios, 
> we can arbitrarily assume that the 3 A voters are in fact attempting 
> strategy. Punishing strategy might not be the worst thing in the 
> world, but rather than punishing 48 voters for the strategy of 3, it 
> would be better to ignore the 3.
>
> I'll write a broader response in a minute.
>
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