Relative and Absolute Power

Tony Simmons bbadonov at
Fri Jun 29 17:14:22 PDT 2001

>> From: Richard Moore <rmoore4 at>
>> Subject: Re: [EM] Relative power


I quickly read the article at about Alan
Natapoff's scheme for computing power.  Apparently, it does
indeed compute power in a sense that doesn't require the
total to be a constant.  That's what I was getting at with my
examples of elections in which none of the voters had any
power at all -- that absolute power needn't be fixed at some
arbitrary total.  That's also why I was asking if he'd taken
into account the effect of each candidate's chance of
winning.  As it turns out, that's what drives his argument.

I think that makes good sense.  I haven't actually seen his
theorem, so I can't say it's valid, but it's what I'd expect.
If I'm voting in the 2000 Presidential election, it makes
sense for me to feel that I have more power if I live in
Florida than if I live in California, at least in the sense
of being more likely to casting the decisive vote.  And given
something reasonably close to that for a definition, I'd
expect total power to vary.

What I'm not at all convinced of is that increasing total
power in that sense has anything close to the significance
Natapoff wants us to believe it has.  Or that it's at all

For example, suppose the League of Women Voters is electing
an Honorary President, and the two candidates are Elizabeth
Cady Stanton and Jack the Ripper.  As it turns out, Stanton
is way ahead in the polls.  Consequently, with only the most
miniscule chance that Mr. Ripper could win, no vote is
anything close to pivotal, and consequently, nobody has any
power in the Natapoff sense.  Now, let's suppose somebody
comes up with a method of counting votes that gives Mr.
Ripper a very well insulated snowball's chance in hell of
winning.  Is this a Good Thing?  Or is the good thing that
Stanton should win because that's who the voters want?

My feeling is, if Stanton is more likely to win, choosing a
system that gives the Ripper a better chance might increase
the total power in the Natapoff sense, but so does anything
that makes the odds of each candidate winning about the same
no matter what the sentiment of the voters.  I don't see how
that can be a Good Thing.

Personally, I think Natapoff has fallen victim to his own
rhetoric.  He is quoted in the article as talking about how
the Electoral College protects the minority from the tyranny
of the majority.  But the fact is, somebody is going to win.
The voters who voted for the winner get their way, and
everyone else doesn't.  If that's tyranny, it's also
unavoidable in a one-seat race.

Natapoff seems to realize this.  He says that the one
unavoidable anomaly of the Electoral College is that
occasionally a less popular candidate will win, but that's
the price we pay for preserving the power of the minority.
Natapoff says the outcome is only temporary, and is fixed
four years later.  But this anomaly isn't really an anomaly,
or a side effect of the difference between the EC and direct
election.  It is the only difference in the outcomes, and if
it's not a benefit, then the EC has no benefits at all.

>> Tony Simmons wrote:

>> >>>From: Richard Moore <rmoore4 at>
>> >>>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.)

>> Obviously there are always trolls on the net, but the
>> article was originally appeared in print media (Discover
>> magazine, 1996). I think the article was meant to be serious
>> and the site linking it also, though the latter definitely
>> seems a bit over the edge as can be seen by looking at some
>> of the other "information" on it.

>> > 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.

Yes, that's an exception to my "total power is constant"
rule. But there isn't really an election or an electorate in
this case, only the illusion of one.

>> > 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.

>> I'm not meaning to criticize the power indices you were
>> discussing. The Natapoff "index" was flawed becasue it was
>> based not on pivotal probabilities of voters in a given
>> state but on the probability that there *is* a pivotal vote
>> somewhere in the country for a given election. But having a
>> pivotal vote turn up somewhere in Florida does little for my
>> voting power here on the west coast. And that pivotal vote
>> doesn't really belong to one voter anyway. If the vote went
>> 5000000 to 4999999, then each of 5000000 voters had a tiny
>> fraction of a pivotal vote.

>> > 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 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.)

>> Well, you can see what my opinion is of that particular
>> article. There are some other references and arguments there
>> but I haven't really looked into them all; some of the few I
>> did look at were absurd. Might be good for a laugh but
>> that's about it.

>> Richard

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