[EM] Best Single-Winner Method

[Chris Benham]

Richard F.,

> (If you are referring to something other than MJ, please specify what 
> it is.) 
I did. Did you mean to refer to MJ?

> On 22/05/2019 3:15 pm, C.Benham wrote:
>
> Richard,
>
> Can you please explain, perhaps with an example, how your "Instant
> Pairwise Elimination" method can possibly "elect a non-Condorcet winner"? 

I don't think Smith set is very hard to explain. But you could even omit 
that and
just say that if one candidate pairwise beats all the others it wins and 
if not we
eliminate any candidate that pairwise loses to all the others and if 
there isn't one
we eliminate the candidate that is lowest ranked on the greatest number 
of ballots
and then repeat the whole process.

This would ensure that the method meets Condorcet (and Smith) and most 
of the
time there will be a CW and a lot of mucking about will be avoided.

Chris Benham


On 23/05/2019 5:23 am, VoteFair wrote:
> On 5/22/2019 1:28 AM, C.Benham wrote:
> > ... I suppose you could have a bottom cycle and a
> > CW who is ranked bottom on the highest number of ballots.
> >
> > That combination would be very very unlikely, but why allow it?
> > Why not use my version?
>
> If you are referring to Majority Judgement (MJ) then my answer is that 
> MJ is difficult to understand -- from the perspective of just using 
> spoken words while talking to someone who does not already understand 
> terms such as "majority" -- not to mention "Smith set" and "Condorcet".
>
> (If you are referring to something other than MJ, please specify what 
> it is.)
>
> Being easy to understand is extremely important -- as mentioned in 
> item number 1 in an earlier message within this thread.
>
> When talking to non-math people, I use the term "pairwise counting" 
> and when someone does not immediately nod their head in recognition 
> then I refer to the analogy of sports teams and the idea that if there 
> is a team that loses every game against each other team then they 
> clearly deserve to be eliminated.? I haven't encountered anyone who 
> hasn't understood that.
>
> Also I find that non-math folks seem to emotionally like the idea of 
> working from the bottom up, eliminating one candidate at a time.? This 
> might be why instant-runoff voting (IRV) is so popular.
>
> If a "rock-paper-scissors cycle" (which most people immediately 
> understand) occurs, I agree that there are better methods for 
> resolving those, but they are more difficult to understand.
>
> I figure if Instant Pairwise Elimination (IPE) gets used anywhere then 
> it will be easy to later transition to something better, such as the 
> Condorcet-Kemeny method, which is mathematically equivalent to 
> VoteFair popularity ranking, which is part of the VoteFair system that 
> I advocate (and which includes proportional representation).
>
> In other words, it would be rare for IPE and Condorcet-Kemeny to yield 
> different winners, so I figure this difference is not worth teaching 
> to non-math people.? IPE gives them something they can quickly 
> understand. And it helps them quickly realize why our current 
> single-winner method is so primitive.
>
> Richard Fobes
>
>
> On 5/22/2019 1:28 AM, C.Benham wrote:
>> Richard,
>>
>> To answer my own question, I suppose you could have a bottom cycle and a
>> CW who is ranked
>> bottom on the highest number of ballots.
>>
>> That combination would be very very unlikely, but why allow it? Why not
>> use my version?
>>
>> Chris Benham
>>
>> On 22/05/2019 3:15 pm, C.Benham wrote:
>>>
>>> Richard,
>>>
>>> Can you please explain, perhaps with an example, how your "Instant
>>> Pairwise Elimination"
>>> method can possibly "elect a non-Condorcet winner"?
>>>
>>> As I understand it, the method eliminates all the non-members of the
>>> Smith set, and then if
>>> more than one candidate remains, next eliminates the candidate who
>>> (among remaining candidates)
>>> is lowest ranked on the highest number of ballots, and then repeats
>>> both steps until one candidate
>>> remains.
>>>
>>> Is that right?
>>>
>>> From the page you linked to:
>>>
>>>> To appreciate how easy it is to understand, here?s a full description
>>>> of the IPE method:
>>>>
>>>> ?*Voters rank the candidates using as many ranking levels as there
>>>> are candidates, or at least 5 ranking levels if ovals are marked on a
>>>> paper ballot and space is limited and lots of the candidates are
>>>> unlikely to win. During counting, each elimination round eliminates
>>>> the candidate who loses every pairwise contest against every other
>>>> remaining candidate. If an elimination round has no pairwise-losing
>>>> candidate then, for that round, each ballot gives one count to the
>>>> lowest-ranked remaining candidate on that ballot, and the candidate
>>>> with the highest such count is eliminated. The last remaining
>>>> candidate wins.*?
>>>>
>>>
>>> Chris Benham
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