[EM] Fwd: Fwd: U/P voting: new name for simple 3-level method.

[C.Benham]

43: A
24: B>C
23: C>B
10: D


On 9/11/2016 4:21 PM, Jameson Quinn wrote:

> I think that scenarios like the above are fundamentally pathological; 
> any possible winner has only minority approval, so that even assuming 
> all ballots are semi-honest, any of them could be a true Condorcet loser.

C: I can't see anything "pathological" about the "scenario". The ballot 
set can be taken at face value.  Presumably the A and D supporters 
simply aren't interested in any candidate
other than their favourites, while the B and C supporters form a tight 
coalition. And B is the clearly voted Condorcet winner.

Just because you can imagine that with less truncation some other 
candidate could have been the Condorcet winner doesn't mean that the 
scenario is in any way "pathological".

> J: Thus, I believe that it's more important for a system to try to 
> avoid scenarios like the above, than to try to find a perfect winner 
> in such a scenario.

But there isn't  (or shouldn't be) anything difficult about finding "the 
perfect winner" in the scenario. B is the plainly voted Condorcet 
winner.  An Approval-like method
might mistakenly elect the "similar" candidate C, but  A and D are out.

And if I agreed that a system "should try to avoid" such a scenario, I 
can't see how it could (allowing 4 candidates and using ballots with 3 
or more ratings slots).

> 43: A
> 40: B>C
> 6: C>B
> 1: C
> 10: D
>
> J:... I think that a case can be made for either A or B. After all, 
> they'd be tied if we try to approximate Score by using truncatable 
> Borda here. But no serious case can be made for C or D, even though C 
> wins MTA and MCA.

The pairwise-dominant B,C coalition is still intact.  Without the 
irrelevant D ballots it has more than half the votes. B is still the CW, 
C is the most approved ("accepted", voted above bottom)
candidate. B is also more approved than A. That adds up to no case for A.

> J: After all, they'd be tied if we try to approximate Score by using 
> truncatable Borda here

C: In my opinion that is a bizarre and very weak standard. Those methods 
don't even meet Majority Favourite, and Borda has other problems.

> J: But no serious case can be made for C or D, even though C wins MTA 
> and MCA.

C:  C is the most approved candidate and pairwise beats all the others 
except B, and all of B's supporters approved of C (which arguably 
somewhat weakens any post-election complaint
they might make, since MTA and MCA  are quasi-Approval methods that 
aren't advertised as meeting the Condorcet criterion.)

Another 3-slot FBC method I think we should be comparing with these 
three is  3-slot TTR,TR  (aka" ICT").  The algorithm is probably too 
complicated to interest Jameson
as a practical reform proposal, but it meets Chicken Dilemma and 
"Majority Condorcet" and easily elects the CW in the recent examples.

> J: One possible alternative default rule: ballots alternate between 
> defaulting to "acceptable" and to "unacceptable". Each ballot clearly 
> states which default it uses, and there is a place on the ballot to 
> globally change that default. (I doubt Chris will like this idea, but 
> it is at least straightforward, explicit, and easy to describe.)

I'm strongly of the view that the voters shouldn't have to bother 
explicitly marking candidates they rate as unacceptable. I suggest a 
ballot instruction something like:

"Among candidates you find acceptable, mark however many you like of 
your favourites as Preferred and the rest as Acceptable".

However, if there was a concern that someone might get access to the 
ballots after they're cast and before they are counted and alter some by 
adding marks to
candidates the voters left unmarked, then that could be justification 
(or a pretext) for a draconian Australian-style solution with a ballot 
instruction like:

"Mark each candidate as one of  Preferred, Acceptable, Unacceptable.  
You must mark every candidate."

Then ballots that don't mark every candidate are declared "invalid" and 
have no effect on the election result.

One more semi-sane alternative is to have a ballot instruction like the 
Australian-style one but make the default "acceptable" under MTA and MCA 
and "unacceptable"
under U/P but in each case with a weight of  one half in the counting.   
(But of course that doesn't completely remove the incentive for some 
cheater to add marks to
ballots).

Chris Benham




On 9/11/2016 4:21 PM, Jameson Quinn wrote:
> 2016-09-10 21:26 GMT-04:00 C.Benham <cbenham at adam.com.au 
> <mailto:cbenham at adam.com.au>>:
>
>     On 9/11/2016 5:02 AM, Kevin Venzke wrote:
>
>         43: A
>         24: B>C
>         23: C>B
>         10: D
>
>         Under MTA the B and C voters are being completely reasonable:
>         They hope for majority approval but can still hope for a win
>         if they
>         don't get it.
>
>         Strategy is less likely to produce these ballots under U/P
>         because the B and C voters are taking a gamble. To get a
>         similar outcome
>         they have to vote B=C. Anyone who doesn't is functionally
>         defecting!
>
>
>      C: A very good example!   Assuming MTA and MCA use Top Ratings
>     scores to break Approval ties, they both elect the Condorcet winner B.
>
>
> J: But both could be shifted to C with a single C-only ballot, even if 
> the B:C ratio were 46:1 instead of 24:23.
>
>
>     C: U/P's under-use of  the middle ratings slot means that it
>     relies more on its "majority disqualification" mechanism which
>     seems to make it more
>     vulnerable to irrelevant ballots, as in the example.
>
>     Under U/P, without the irrelevant D ballots, A and D are
>     disqualified and B is the glorious winner. With them, B and C and
>     D are disqualified and  (without needing
>     any others to be disqualified) A wins.
>
>     This causes me to reject U/P as clearly worse than MTA and MCA. Of
>     the three I (again) rate MTA as the least bad.
>
>
> J: I think MTA is pretty darn good. I still prefer U/P.
>
> I think that scenarios like the above are fundamentally pathological; 
> any possible winner has only minority approval, so that even assuming 
> all ballots are semi-honest, any of them could be a true Condorcet 
> loser. Thus, I believe that it's more important for a system to try to 
> avoid scenarios like the above, than to try to find a perfect winner 
> in such a scenario. In fact, in the related scenario:
>
>
> 43: A
> 40: B>C
> 6: C>B
> 1: C
> 10: D
>
> ... I think that a case can be made for either A or B. After all, 
> they'd be tied if we try to approximate Score by using truncatable 
> Borda here. But no serious case can be made for C or D, even though C 
> wins MTA and MCA.
>
> Anyway, I think U/P does a better job trying to discourage the kind of 
> strategy that would lead to a scenario like the above. And part of 
> that is the default rule which Chris has criticized.
>
> One possible alternative default rule: ballots alternate between 
> defaulting to "acceptable" and to "unacceptable". Each ballot clearly 
> states which default it uses, and there is a place on the ballot to 
> globally change that default. (I doubt Chris will like this idea, but 
> it is at least straightforward, explicit, and easy to describe.)
>
>
>
>
>
>
>

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