[EM] Description of "Median," my Approval variant

[Forest Simmons]

On Thu, 6 Mar 2003, Forest Simmons wrote:

>
> (8) We could combine your method (2) with method (6), by finding the max
> of each row in your (transpose of pairwise) matrix and then subtracting
> the min of the corresponding column.  The candidate corresponding to the
> minimum such difference would be the winner.
>
> [Note that this is similar to MinMax (margins) but with the subtraction
> done after the row and column max and min operations.]
>
> This combination method (8) would take care of the anomalous results at
> the end of your message.
>
> Note for example, that disaster associated with
>
> 1000: A, 1000: B, 1: AC, and 1: BC
>
> is avoided by taking into account the offensive prowess of candidates A
> and B in comparison to C who is relatively strong defensively but weak
> offensively.
>
> In general method (8) doesn't always pick the beats all winner.  I don't
> know if it does when restricted to ballots of resolution two (i.e.
> approval ballots).  I suspect there may be some cases where it doesn't
> pick the approval/beats-all winner (which is not necessarily a defect in
> this context).

In fact, your first example still works under this modification:

Your respective row maxima were 15, 19, 22, and 27.

Your respective row minima were 10, 12, 15, and 9.

The respective differences are 5, 7, 7, and 18.

So A is the winner by the modified median method!

Also, I believe that your median method and the modified median method
both satisfy the FBC.

Forest