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

[Abd ul-Rahman Lomax]

At 10:27 PM 3/30/2008, Dave Ketchum wrote:

>Runoffs main value is recovering from a methods weaknesses until 
>something can be done about the method.  They are too expensive to 
>be accepted as if a normal part of a usable method.

What is missed here is that the basic requirement for an election 
method to be truly democratic is that the result actually be accepted 
by a majority of those voting. Runoffs are a device for doing this, 
and, as implemented, they are even better than they might seem, 
though taking advantage of the facility is rare. In many runoffs, the 
voter can write in a candidate, still. Thus it is theoretically 
possible for another candidate than the top two to win. But with 
Plurality, this trick is dangerous; only if there is a true majority 
requirement, enforced through as many ballots as it takes, is there 
real democracy. Anything short of that is a compromise.

The problem is much more soluble than might appear. Elect 
representatives, through methods that insure that everyone or almost 
everyone is represented. Then the assembly of representatives elects 
officers. Parliamentary system. Democratic. Note that the U.S. 
started out with something like this, but it was corrupted and 
perverted by the party system and the fact that the Constitutional 
Convention just couldn't work out better rules for the selection of 
electors. Further, not having proportional representation in the 
House made it all the quirkier.


>>>I object to calling this example "likely" - think of such as 16 
>>>with 3 Ys together with ZERO 4 Ys.
>>
>>Yes, but. Think of 100016 with 3 Ys together with 100000 with 4 Ys.
>>That is, add 100000 to all position counts and thus to all vote 
>>counts. The results are the same. It looks drastic because the 
>>election has been boiled down to the *margins*.
>>Note that if positions are random, we would expect 4 occurrences of 
>>3Ys for every occurrence of 1 Y. It is like the number of 
>>occurrences of coin toss patterns. If we throw a coin many times, 
>>and count the occurrence of each sequence of four, we will get 
>>these patterns of equal probability:
>>YYYY
>>YYYN
>>YYNY
>>YNYY
>>NYYY
>
>Without arguing the exact validity of the above, the following 
>combinations in the test case were stretching expectability:
>      16 3Y with 0 4Y
>      4 3N with 5 4N
>
>And, again, Plurality did not fail - it simply responded neutrally 
>to the collection of votes.

Plurality awards the win to the candidate with the most first place 
votes, since that it all it detects. As shown, it is quite possible 
that this candidate is not at all the best candidate, and that, in 
fact, a majority of voters would agree.

What I wrote above was simple, and it addressed the exact situation 
that Ketchum then responded with. The sequences I have were the 
sequences with 3 and 4 Y votes; the point was that there were many 
more 3Ys than 4Ys (i.e, 4 vs. 1) and this would hold with large 
numbers of voters with random positions. Ketchum had asserted that 
there was something unlikely about there being 4 and 0. And I pointed 
out that this is actually only one vote different from the most 
common pattern. The odd one is at the other end, where there are 4 3N 
votes and 5 4N votes. The latter is five times the expected number. 
But the sample is small and that kind of deviation would not be 
terribly unlikely, and, if we see the scenario as being a reduction 
by subtracting 100,000 votes from each total, what we really have is 
an even distribution with very small deviations. (the deviations in 
such a large sample would be expected to be larger than than, in fact.)

But, again, the point was that the election is a possible one, not 
that it was a probable one. It illustrates what *can* go wrong with 
plurality, not what would *usually* go wrong.

It's really simple: to repeat, with sincere voting and a large field 
of candidates covering all positions, Plurality is quite unreliable, 
and this is known and seen in real elections. Because of the politics 
of it all, plurality still works, usually. But definitely not 
reliably. It can easily pick a candidate who would be rejected by a 
large majority in favor of another candidate in the race.

>One more time:  Plurality reports what the voters vote.

That's kind of an oxymoron. All functioning election methods "report 
what the voters vote," though some report more than others. Some 
allow voters to express much more information, Plurality is about the 
minimum possible.

>>However, Range would always choose YYYY. It was *designed* to do that.
>>Always. If voters vote sincerely.

And Bucklin, at least in the example studied, likewise chooses YYYY, 
whereas IRV, ranked according to certain assumptions, chose a 3Y 
winner. Not bad, not optimal.