Always impossible! - not
ntk at netcom.com
Wed Jul 15 20:03:47 PDT 1998
I agree with Demorep that it isn't a good thing to give more voting
power to a rich voter than to a poor voter. No chance that would
be adopted; it would be abhorrent to voters & voter-interest groups.
I'm rather surprised that it would be proposed.
But, Demorep, do you have to use the expression "1-person-1-vote"?
That's another way of saying the method has to be Plurality, or
maybe IRO, though it would admittedly permit Plurality With Withdrawals
and IRO With Withdrawals.
"1-person-1-vote" is used to argue against rank-balloting counted
pairwise, and against my easy, but maybe a little cowardly,
Approval proposal, and related point systems. How about, instead,
saying "equal voting power for each voter".
Incidentally, Saari, you may feel that $10 is cheap, but what
if there are many candidates in the election, and it isn't obvious
that any two are the most likely to tie. A voter would want to,
but maybe not be able to afford to, give those triple votes to
a number of candidates. Voting then is getting too expensive.
I've voted in elections with well over 10 candidates, for instance.
And it isn't true that merely charging for the votes will make
people vote sincerely. It's still true that it's in your interest
to give your hard-earned votes where they'll do you the most
good, and that doesn't necessarily mean giving them to your
favorites, in proportion to their utility. It means giving them
to the candidates with the greatest strategic value. If you can
afford only a limited amount of votes, and there are a number of
candidates with positive strategic value, then you'll want to give
free votes to all of them, and double votes to all of them if
you can afford to, and triple votes to them if you can afford to.
If you can only afford a few triple votes, then you'll give them
to the candidates with highest strategic value. Wait, I'm sorry--
the rules you describe don't permit giving someone a free vote,
a $1 double vote, and also a $10 triple vote, do they? In that
case, give the biggest you can afford to as many as you can afford
to, among those with positive strategic value, starting with those
with highest strategic value. Then give the next biggest to as
many as you can afford to, with highest strategic value. Of course
eventually everyone who hasn't gotten a bigger vote from you will
get a free single vote from you if their strategic value is positive.
The scheme I described would elicit more sincer voting.
But maybe your share of the responsibilitly for electing someone
should be determined by dividing your vote difference between
the top 2 by the total amount of difference between them voted by
everyone who voted the winner over the 2nd place winner. Multiply
that by your vote difference between the top 2, and that gives
the amount by which you've improved your utility by voting.
If you exaggerate by voting too large a vote difference between
those 2, then you'll be charged more than your vote has gained for
you, and so that's a loss. Of course you can _under-represent_
that utility difference between those 2, or you can save by not
even voting. But since outcomes that you like are worth something
to you, wouldn't there be incentive to pay what it's worth by
voting sincere ratings?
Again, I _don't_ propose this. The problems in adjusting the
charges for different people would be horrendous. Not just income
would have to be considered, but also job prospects, upward mobility,
education, children, substance habits, debts, etc., etc. Forget it.
Sure, if it could be done fairly, no one would have any reason to
object. But that's virtually impossible. And who'd be setting the
No, forget about preference intensity measurement by paying.
Someone suggested that it could be done by only allowing each
person a fixed amount of "play money" for a period of many
elections. Maybe, but then you've got to take into account
life expectancy, and, if the next election is more important,
then people will squander their play money on that. I don't
like that either. The play money idea would properly be used
with the cost procedure that I described earlier (unless I didn't
describe it right; the book I named describes it better in that case).
The "play money", or free long-term payment supply, would solve the
income adjustment problem, but I still don't like that approach,
and prefer simply using a good strategy-free rank-balloting method,
or, failing that, giving everyone a point (or several points) to
give or not give each candidate (Approval or Cardinal Measure).
By the way, that demonstration I talked about earlier, involving
a graph and its slope, actually all that did was suggest (not prove)
that the two quantities are linearly related on that small interval.
That doesn't show that they're _proportional_, as I mistakenly said
Fortunately that assumption isn't needed for that discussion
about all or nothing points, or for calculating optimal strategies
for Approval & Plurality & Cardinal-Measure.
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