[EM] Formulas for strategic fractional rating (SFR)

[Michael Ossipoff]

As I was saying, the idea of SFR is for A voters to give to B a
fraction of max rating, just enough to help B to beat C and win, if
certain conditions are met.

A, B, and C stand for the votes, or vote-percents, of candidates A, B, and C.

The obvious way to choose the fraction, f, of max points to give would
be to just assume that the factions will have the same percentages of
the vote that they had in a previous election or poll.

So, to make B beat C, then, you need:

B + Af > C

f > (C-B)/A

But, if you like B, and trust the B voters a little, then maybe that
formula seems a little stingy. After all, you'd like to help B to win
for you if the B faction is bigger than your A faction.

So maybe assume that A and B are equal. That they're both equal to
their average in that previous election or poll. Let "av" stand for
that average. Then:

f > C/av -1

Or maybe, if you know that it's just a 3-candidate election, and you
have an estimate, N, of what fraction of the electorate the A voters
and B voters add up to, then:

f > 2/N - 3

Ideally, you'd like to help B to win if B > A. Maybe sometimes you'd
assume that B and A are both equal to what A was in the previous
election or poll, or what A was in the previous election or poll.

Using the average, as described above, implies an assumption that one
candidate is gaining votes lost by the other candidate.

But you could make any assumptions or estimates about how votes will
move between different candidates. Those assumptions could be used for
the first approach described in this post.

Or you could judge what vote migrations, from what candidate to what
other candidate, would be the most likely to make A and B equal, and
base a SFR formula on that.

For example, in the 2008 presidential poll at minguo, these candidates
received the following numbers of top ratings:

Obama: 99
Ron Paul: 74
Dennis Kuccinich: 66

If you prefer Kuccinich to the other two, and you want to give SFR to
Paul, as a strategic compromise, then by the first assumption and
formula described in this post, you'd give to Paul .38 max, as SFR.
Maybe a little more, of course.

But what if you wanted to make Paul outpoll Obama if Paul will have
about the same support as Kuccinich--and you assume that, for
Kuccinich's faction to be as large as that of Paul, it will get its
new voters from the other Democrat. So, for Kuccinich to gain the 8
votes needed to equal Paul, Obama loses those 8 votes, and now has 91
instead of 99. Now Paul only needs 17 votes to equal Obama. That could
be achieved if the (now) 74 Kuccinich voters each gave to Paul .23
max, as SFR.

So someone who prefers Kuccinich to the others of those 3 candidates
might (by these assumptions) give Paul .38 max, or .23 max, depending
on whether s/he prefers to assume that the vote configuration will be
like it was in 2008, or whether s/he prefers to optimistically  assume
that Kuccinich can equal Paul's points total and has a chance of
winning.

I made the latter assumption, and gave to Paul 2 points, in the 0-10
Score ballot.

You might say that if someone assumes that the vote-configuration will
be like 2008, than that voter should give max points to Paul, since
Kuccinich can't win. But that vote-configuration assumption is made
only for the purpose of judging how much Paul needs to outpoll Obama.
Of course you aren't really sure the numbers will be like that, and so
you might not want to give max to Paul, because, for all you know,  it
might not really be like that, and Kuccinich could have a win. Hence
the .38 max SFR, under those assumptions.

These f choices are, of course, based on assumptions, rough
approximate guesses, and subjective choices. But, thereby, you're at
least doing something to help a compromise without unduly giving away
the election to him/her, to the extent that you might be, had you
given them max points.

Mike Ossipoff