[EM] Borda expectation

[MIKE OSSIPOFF]

EM list:

As before, I start with that unwritten standard factor as
Pij, and then adjust the result afterwards for how the method's
conditions differ from the ones that are assumed by that standard
probability factor.

So, without Pij, the utility expectation change for each
pair vote diifference is (Vi-Vj)(Ui-Uj).

There are 3 candidate pairs that you vote between, and so
the above expression is used in 3 terms:

1(Ua-Ub) + 1(Ub-Uc) + 2(Ua-Uc)

[You're voting a double vote-difference between A & C].

Collecting terms, that is: 3Ua-3Uc

Since Ua is 1 & Uc is 0, that expression equals 3.

But, when we adjust for the fact that a greater total number
of vote-difference is voted in Borda, by each voter, because,
on the average, each voter votes a vote difference of 4/3
per candidate pair, we have to multiply that 3 by 3/4, and
we get 9/4 = 2.25

So 2.25 is Borda's table entry.

Mike Ossipoff

______________________________________________________
Get Your Private, Free Email at http://www.hotmail.com