[EM] RE: ICA (correction)

Simmons, Forest simmonfo at up.edu
Wed Sep 14 15:09:01 PDT 2005

I meant to say that you could use matrices M and PM (not CM) to formulate ICA, in the last paragraph quoted below.
Sorry for the confusion.

I suggest that we consider methods that sum two modified pairwise matrices in addition to the basic pairwise matrix:

(This description is at the ballot level)

In the ordinary pairwise matrix M, the (i,j) entry is a one or a zero depending on whether or not candidate i is ranked ahead of candidate j on the ballot.

In the "Pro modification"  PM,  if candidate i is ranked equal first, then row i is filled in with ones.

In the "Con modification" CM,  if candidate k is truncated, then column k is filled in with ones. This is Ossipoff's "power truncation" matrix.

I'll leave it as an exercise to restate the definition of ICA in terms of  M and CM, assuming that "least approved rank" is treated like a candidate.

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