[EM] Seven +/- Two

[Forest Simmons]

Recently I suggested some high resolution ideas that haven't generated too
much excitement. I thank Roy for contributing some thoughtful responses
along those lines. 

It reminds me of when Richard came up with Majority Potential, a great
idea as a standard of comparison, but not immediately adaptable for public
consumption, therefore put on the back burner.

So perhaps we should work at the other end.

Let's start with one bit per candidate and work up.

If the ballot allows the voter one bit of expression for each candidate,
what's the best we can do?

I think most readers of this list would say that Approval is the method
that makes the best use of that bit. [Marked=Yes=Approved,
Blank=No=Unapproved] 

Be that as it may, let's go to the next most complicated ballot, the two
bits per candidate ballot.  Each candidate has two ovals to the right of
her/his name.  There are four possible combinations of Blank and Mark. If
we represent the blanks with zeros and the marks with ones, we see that
the four combinations are  00, 01, 10, and 11 .

A sample ballot might look like this (without the accompanying
instructions):

Joe Aiojiof   () ()
Helen Gklsd   () ()
Janice Piuh   () ()

A blank oval is considered to be a zero, while an Oval with any kind of
mark in it is considered to be a one.

So the ballot comes with default votes of 00 for every candidate.

Now, what instructions should be included on the ballot?

That depends on what the two bits are supposed to represent, which in turn
is inextricably intertwined with the process of determining a winner from
the set of voted ballots.

The first possibility that comes to mind is that the four possible
combinations should represent the numbers zero, one, two, and three,
respectively, in binary notation.

But they could just as well represent the numbers zero, one, ten, and
eleven in the base ten system that our voters are more familiar with.

In that case (and in any case where the number base is greater than two) 
we have some differences in gap size that we might take advantage of: 

00 < 01 << 10 < 11

As denizens of the information age we all know that there are many other
possible messages, some numerical and some not, that can be encoded with
two bit representations.

Suppose, for a moment that we decide to assign numerical values to the
codes in a way that is order consistent with the above numerical
suggestions, so that the list 00, 01, 10, 11, is in increasing order.

An obvious way of using numerical information is in considering the
numbers as ratings, and giving the win to the candidate with the highest
mean (alternately, median) rating.

But this usage (whether mean or median based) is strategically equivalent
to Approval; our extra bit is largely wasted because the temptation is so
strong to vote only at the extremes 00 and 11. (The second bit is made a
slave to the first.) 

Of course, we could build in some constraints that disallow this kind of
slavery, but such constraints should be in the form of incentives rather
than decrees, in my opinion.

This suggests using the order information in the ballots to find a
pairwise beats all winner. 

I like this idea, but it still leaves the question of what to do when
there is no beats all winner.

Before I give too many of my opinions on this subject, I would like to
hear some ideas from other readers of the EM list.

What's the best way to use the two bit per candidate ballot?

Once we've answered this question, then we can graduate to three bits, and
above, up to seven +/- two bits  :-)

Forest