[EM] Fair and Democratic versus Majority Rules

[fsimmons at pcc.edu]

How did this thread get side tracked to Proportional Representation?

Proportional Representation only works for multi-winner elections.

Of course, everybody knows that PR is the way to go in multi-winner elections. 
And why is that?  Because it solves the tyranny of the majority problem in that
setting.  

So why cannot we see that this same problem exists in single winner elections? I
suggest that the analogous remedy in the single winner setting is proportional
probability.  The simplest method that accomplishes this is random ballot.  But,
as I suggested, there are better stochastic methods that yield probability
distributions with less entropy while still solving the tyranny of the majority
problem..

Jobst's original challenge was something like this (numbers in parentheses are
sincere range values):

60 A(100) , B(80), C(0)
40 C(100), B(80), A(0)

Assuming rational voters and a complete information environment, any
deterministic method including range or approval would elect A even though B is
the sincere range/approval winner, and the clear consensus candidate.

On the other hand, (still assuming rational voters with perfect information) any
decent, proportional probability, stochastic method would elect B with 100%
probability.  

Sometimes only a stochastic method can reliably elect the sincere range/approval
winner.

Note that random ballot is not adequate; it would give alternative A three to
two odds of winning over C, and B would have zero probability of winning.  

So when I say "decent" stochastic method, I'm talking about something more
sophisticated than random ballot.  Jobst has invented a number of such methods.
 The one I mentioned in the first post in this thread is a method I designed to
handle several factions with multiple local consensus opportunities, for example:

20  A1>C!>C3
25  A2>C1>C3
30  B1>C2>C3
25  B2>C2.

Depending on the relative utilities of the various C's, the best solution could
be (among other possibilities) either (1) the random ballot lottery
20%A1+25%A2+30%B1+25%B2, or (2) 45%C1+55%C2, or (3) 75%C3+25%B2.

A decent proportional probability stochastic method will make insincere ballots
backfire, and will automatically assign the appropriate probabilities in all
such cases.

I hope there is some interest in the original intent of this thread.  If not, at
least we had a good talk about PR:)

Forest