[EM] Relative power
Tony Simmons
bbadonov at yahoo.com
Wed Jun 27 20:49:27 PDT 2001
>> From: Richard Moore <rmoore4 at home.com>
>> Subject: Re: [EM] Are voters in larger or smaller states more powerful?
Richard,
Just an observation: There are some people who post stuff on
the Internet that isn't, um, quite valid. I suppose you've
seen or at least heard of the proofs that NASA faked the moon
landings? (And there was one wonderful site that had a
picture in which they are refueling the lunar rover; the
shadow of the vehicle goes in one direction, and the shadow
of the pump at the gas station goes the other way, showing
there must be two light sources, so it couldn't be on the
moon.)
How about this election method: Everybody writes whatever
they want to on the ballot papers. Then the election board
puts slips in hat, one candidate to a slip, and a gorilla
picks one slip out of the hat. Whoever is named on that
slip wins. In this system, nobody has any power, in the
sense of making a difference in the election, because nothing
on any ballot has any effect. Total power = 0.
Or consider this system for electing a monarch: When the
reigning monarch dies, abdicates or is chased into exile by
an outraged populace, there is a rigid system for choosing a
new monarch. Everyone votes (except that anyone who has any
chance of actually becoming the monarch is not allowed to
vote), and then the ballots are thrown in the trash and the
rigid rules determine the next monarch. Again, nobody has
any power because no voter has any chance of influencing the
election.
If I recall correctly (I'm really feeling too lazy to look it
up at the moment), the power indices discussed here recently
are proportions, normalized so they always add up to one.
Ergo, total power is invariant as long as the denominator is
not zero.
One thing I've noticed about the power indices is that they
don't take into account the actual probabilities of
particular candidates actually winning. If all candidates
are running neck and neck in the polls, then it would seem
that each voter would have a pretty good chance of making a
difference. On the other hand, if Stalin is running against
Tsar Nicholas, maybe no voter has much chance of influencing
the outcome.
Is the argument at presidentelect.org worth looking at? (If
there's anything about how the astronaut's face shouldn't be
illuminated when he's facing away from the sun, I'd rather
not take the time.)
>> As a side note to this discussion: Several months ago I
>> found the article
>> http://208.245.156.153/archive/output.cfm?ID=907 which was
>> linked to from the presidentelect.org web site. The
>> article describes a mathematical theory, which I believe
>> is flawed, to the effect that the electoral college
>> increases the power of all voters.
>> I can't find my response, but at that time I sent an e-
>> mail to the presidentelect.org site's maintainer to
>> express my disagreement with the article.
>> The essence of my response was that I found the concept of
>> voting power used in the article (which describes the work
>> of one Alan Natapoff) to be ill-founded. The article
>> states, "In a fair election, he saw, each voter's power
>> boils down to this: What is the probability that one
>> person's vote will be able to turn a national election?
>> The higher the probability, the more power each voter
>> commands." Specifically, I wrote that the sum of the
>> voting power of the electorate must be a constant, since
>> only one decision is being made per election. You cannot
>> increase the voting power of everyone in the electorate by
>> increasing the probability in question, you can only
>> redistribute that power. Any conclusion based on the
>> Natapoff standard would have to be suspect.
>> Another quote: "Natapoff agrees that voters should have
>> equal power. "The idea," he says, "is to give every voter
>> the largest equal share of national voting power
>> possible." Here's a classic example of equal voting power:
>> under a tyranny, everyone's power is equal to zero.
>> Clearly, equality alone is not enough. In a democracy,
>> individuals become less vulnerable to tyranny as their
>> voting power increases."
>> Umm, not everyone's power is equal to zero in a tyranny.
>> The tyrant certainly has greater than zero power. What's
>> more, by the Natapoff standard, it would appear that voter
>> power is maximized in dictatorships and in random ballot
>> voting methods!
>> I also commented that I couldn't believe it took twenty
>> years (as stated in the article) to come up with such a
>> weak theory.
>> Of course, my arguments were completely ignored.
>> The EC must go.
>> Richard
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