[EM] Linear Spread Median Range Voting

[Abd ul-Rahman Lomax]

At 07:48 PM 12/20/2005, rob brown wrote:
>I like this way better than "regular" range voting, as it removes a 
>large part of the incentive people have to vote insincerely.
>
>Still, a voter has to take a guess as to what vote will be most 
>effective in helping to achieve what he wants.  Example:  I vote A: 
>0, B: 55, C: 100.
>
>Then the final score comes out to be A: 56.001, B: 56, C: 45.

>Oops, my vote of 55 for B actually lowered his score, and in this 
>very tight race may have actually cost him the election.

Not exactly. Yes, the vote for B lowered the median by a tiny 
fraction, but, unless this was quite a small town, probably not as 
much as .001.

>  My A and B votes effectively cancelled themselves out in the A-B 
> race, even though I much prefer B and would have liked to help 
> him.  If I had watched the polls more closely, I would have given B 
> a higher score (anything over 57 would have done it), since C 
> turned out to be irrelevant anyway.

You would presumably know enough to know that A was roughly as 
popular as B. (This is a *really* close election, they are not all 
that common.) You'd probably have seen polls that A and B were going 
to get in the range of the mid-fifties. So you did cut it close 
rating B as 55, if it was so important to you that B win.

If you have strong preferences, with median Range -- though the 
method is not really well defined yet -- you might want to vote 
nearer the extremes, just to be safe. So your vote might have been A, 
0; B: 80; C: 100.

median Range much more resembles a ranked method. But I certainly 
have not worked out all the implications, nor am I confident at all 
that the method is sufficiently well defined for optimum performance. 
The latest thought, for example, is that the rating spectrum for a 
candidate would be normalized. I don't know yet whether or not that 
is a great idea or a fish bicycle. Probably the latter. Individual 
ratings might be normalized, which would have a stronger effect. 
Examples showing median Range to have problems, so far, have involved 
truncated ratings; i.e., the voters did not vote the full range; thus 
their preferences were weakened and it is thus made to appear that a 
majority-favored candidate lost to one with less preference.

>Personally, I will never get behind a method that gives a 
>significant advantage to those voters that are better at guessing 
>who is likely to win, and this method does that (as does approval).

This method does that far less than Approval.

Mr. Brown and I differ on the philosophy behind elections, quite 
significantly. In my view, the ultimate "advantage" to the individual 
voter lies in the election of a candidate who has the broadest support.

As an extreme, one may win the election and lose the insurrection. 
(With most insurrections, nearly everybody loses.)

>   People should only need to learn about candidates, not have to 
> fill their brains with strategy and polling data, IMO.
>
>Anyway, if you are gonna have Range voting, this way of figuring it 
>is a huge improvement in my opinion.  The linear spread thing seems 
>to be a simple solution to the likelihood of ties problem.  Don't 
>like it, but dislike it less. :)

It *does* solve the problem of ties. But there are other aspects that 
need attention.

I'm suspecting that normalizing all the votes may turn out to 
optimize the results. As a wild guess, it may make median range into 
a Condorcet-compliant method.

Of course, there is the short-cut to Condorcet-compliance. The Range 
ballot is interpreted as a ranked ballot, and if there is a Condorcet 
winner, that is the winner. If there is a cycle, then the spread 
median Range winner among the members of the Smith set is the winner.

And there is another option: if the spread median winner is not the 
Condorcet winner, then there is an actual runoff between the two. The 
costs of running runoff elections is greatly overstated, compared to 
the benefit of optimizing the satisfaction of the electorate in the outcome.

If your candidate B loses to A in a 2-way race, presumably you would 
not regret so much having rated B almost exactly at the median. Or, 
indeed, if B wins. Your vote would certainly rank B above A in the 
Condorcet aspect of the election.