[EM] New Criterion

C.Benham cbenham at adam.com.au
Fri May 23 23:37:04 PDT 2014

```The example I gave below is also an example of failure of  Unburiable
Mutual Dominant Third.

I'd like to suggest a simplified and generalized version of that,
"Strategically Invulnerable Mutual Third" (SIMT):

*If a set S of candidates are all voted above all non-S candidates on
more than a third of the ballots, and if all the S
candidates pairwise-beat some non-S candidate X, then X can't win.*

This implies compliance with MDT, and means that a sincere MDT winner is
invulnerable to any sort of "offensive" strategy.

ER-IRV(whole) fails Mutual Dominant Third (MDT).

05 A=C
31 A>B
34 B>A
30 C>B

B is voted above all others on more than a third of the ballots and B is
the CW, but  ER-IRV(whole), aka AIRV, elects A.

Chris Benham

On 5/21/2014 2:01 PM, C.Benham wrote:
> 45 A=C (sincere is A or A>B)
> 35 B>A
> 20 C>B
>
> B is the sincere IRV winner (and sincere CW), but if the method is
> ER-IRV(whole) then B is eliminated and A wins.
>
> (This example also works if you change the 45/35/20 numbers to, say,
> 49/48/3).
>
> Chris Benham
>
>
>
> On 5/21/2014 4:29 AM, Michael Ossipoff wrote:
>> Chris:
>> ER-IRV(whole), I've always referred to as "Approval IRV", or AIRV.
>> For the Green scenario, I'm not botherd by IRV's failure of Condorcet
>> and FBC, for reasons that I've given (vastly different media and
>> electorate than we have now in the U.S.)
>> We should all assume that we're in a mutual majority, because (as
>> I've said) we'll be in one if our assessments are right, and if
>> others' judgement is as good as our own.
>> So, in the Green scenario, I'm not so concerned about the strategy
>> problems of voters who aren't in a mutual majorty (MM).
>> IRV is great for you if you're in a MM. Additionally, as you've
>> mentioned, IRV meets LNHa and LNHe.
>> So I don't think IRV needs any mofification, and IRV, without AIRV,
>> would be fine.
>> But I like Benham and Woodall because their Condorcet Criterion (CC)
>> compliance makes things less strategucally drastic for vorters who
>> aren't in a MM. Not that that's important; but it's a nice little
>> luxury, just in case the GPUS voters are convinced by their party's
>> advice, to rank the Democrats directly below GPUS, resultng in the
>> progressives not being a voted mutual majority.
>> ...And, for that same reason, I like AIRV, because its option of
>> approval-like voting (voting Compromise in 1st place along with
>> Favorite) makes things easier for non-MM voters.
>>  Could you give an example of the use of AIRV's pushover strategy?
>> Mike
>
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```

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