[EM] Relative power

[Richard Moore]

Tony Simmons wrote:

>>>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.)


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 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.)


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