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

[Warren Smith]

>  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.

-- 
Warren D. Smith
http://RangeVoting.org <-- add your endorsement (by clicking "endorse"
as 1st step)
and
math.temple.edu/~wds/homepage/works.html