[Election-Methods] YN model - simple voting model in which range optimal, others not

[Dave Ketchum]

Looking closer, I tripped on this one:
 >>      Note that YYYY will now attract the same 5 voters who had gone for
 >> NNNN, and the new NNNN will get 0 votes.

Saying it more carefully:
 >>      Note that previous YYYY, now labelled NNNN, will attract the same 
5 voters who had gone for NNNN, and the new YYYY will get 0 votes.

I did change some details, and kept some the same:
      Candidate labels are inverted, Y vs N.
      Voters look for the SAME Y vs N candidate names.
      Thus the 5 winning votes go to the formerly YYYY candidate who is 
now labeled NNNN.
      But this is a side issue.

Plurality is FULLY capable and neutral in an example such as here where 
voters approve ONE of a collection of candidates.

We want to move to more capability when we realize that it matters that 
Plurality cannot satisfy desires such as to "approve all who are Y to both 
issues 1 and 2".

DWK

On Sat, 29 Mar 2008 15:18:14 -0400 Warren Smith wrote:
>> Building on those thoughts, let's try something with Plurality:
>>      Start with that collection of voters and issues.
>>      Invert all the issues so that a Y will attract the same voters as an
>> N did, and an N will attract those who had gone for Y.
>>      Note that YYYY will now attract the same 5 voters who had gone for
>> NNNN, and the new NNNN will get 0 votes.
>>      The collection of voters, while owning no claims to randomness,
>> remain as legitimate as they had been.
> 
> 
> --true.   However, you seem to think this
> means now plurality-voting looks better.  That is not so.
> 
> In your new scenario, each issue is won by "N" by majority vote.
> But plurality gives the election to the worst winner YYYY
> and gives zero votes to the best candidate NNNN.
> 
> Plurality still looks maximally bad in your new scenario.
> These inversions really never change the picture.
> 
> ----
> 
> I managed to prove some more theorems  In the YN model with
> random voters and canonized issues.
> Plurality and approval voting both will elect a candidate with more than 50% Ns
> in his name (i.e. a quite poor one) at least a constant fraction of
> the time;  Condorcet
> cycles will exist asymptotically 100% of the time.
> I do not know how Borda, Condorcet, and IRV will behave
> in the random-voter YN model.   Computer simulations seem called for
> since my unaided mind is not solving that.
-- 
  davek at clarityconnect.com    people.clarityconnect.com/webpages3/davek
  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
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