[EM]

[Alex Small]

Josh wrote and Demorep replied:

>>Is there any way to sum the House and Senate over/under representation
>>figures?
>
>D- It depends a bit.
>
>Votes for losers in gerrymander/ plurality areas are obviously ALL
>*wasted*--under-represented votes.
>
>Votes more than the votes for the second place choice are *wasted* (though
>unknown before the election). (with the winner getting a plurality only or
>a majority).
>
>Thus -- it depends on how one looks at the math.

My take on Josh's question was that he wanted to know if there's a way of
saying "Overall in Congress, state X has twice as much representation per
person as state Y."

In a bicameral legislature comparing the power of each state is tricky.  I
don't know if you were on the list when I proposed an axiomatic approach to
the Electoral College.  Briefly, you can't always say that the power of a
bloc is proportional to how many votes it has.  If 4 states each had 100
votes and 1 state had 1 vote, if the quota is a majority of votes (201) and
each state votes en bloc then the tiny state has just as much power as the
others.  Any combination of 3 states will suffice.

Using my axioms (look for a post called "Electoral College:  Axiomatic
Approach" or something like that) if we generalize to Congress, a large
state always has more power than a small state (assume that each state's
Hous delegation votes en bloc, because that means the state brings all of
its potential power to bear).  The reason is that there may be situations
where a bill needs just 2 more votes in the Senate but 10 more votes in the
House.  Any state can give 2 Senate votes but not all states can give 10
House votes.  So one-on-one large states have more power.

To quantify absolute power, rather than just establishing a ranking order,
is impossible in our Congress.  The reason is this:  Look at two state with
identical numbers of Reps, and compare them with larger state that has more
Reps than those two combined.  There are situations where those two small
states can turn the tide but the big state can't (because the bill needs 4
more Senate votes) and there are situations where the big state can turn
the tide but the two small states together can't (because the bill needs
more House votes than those 2 can muster).

It's really dubious to say that those two small states have equal power to
the large state, or less power, or more power.  If for any situation where
the two small states could turn the tide the big state could also do so,
and vice versa, we could say that the small states (which have equal reps
and hence equal power) have half of the power of the big state.

It may be tempting to say that since there are times where the big state
matters more than the two small states, and times when the two small states
matter more than the big state, they are equal.  Here's the problem:
Suppose the two small states are Alaska and Rhode Island (1 Rep each) and
the big state is Texas.  We could also say that Alaska and Rhode Island
combined are stale-mated with California.  If we say that CA is equal to
{AK, RI} and TX is equal to {AK, RI} does that mean that CA and TX are
equal?

Not if we want equality to be transitive.  There are obviously cases where
CA can turn the tide but TX can't, but there are no cases where the reverse
holds true.

Point is, it all becomes a big mess, and it's hard to say that CA has twice
the power of some other state or whatever.  Hence it's really hard to
measure Congressional power per person in absolute terms.  We can measure
Senate power per person or House power per person, but not Congressional
power per person in each state.

Alex