[EM] Participation

[fsimmons at pcc.edu]

Markus pointed out that Bucklin fails mono add top.  Now I see why.  If x is
ranked second on all of the ballots except the new one, and some other candidate
y has exactly 50% first place support, then one ballot of the form x>y will
change the Bucklin winner from x to y, because now the collapse to second rank
is unnecessary..

So we let's state a special version of participation that Bucklin satisfies:

If x wins Bucklin by collapse to level k, then adding a new ballot cannot switch
the winner from x to y unless y is ranked above level k or x is ranked below
level k.

In other words, the new winner has to be ranked relatively high to k or else x
has to be ranked relatively low to k in order to change the winner.

This seems like a reasonable Participation criterion.  It should be enough to
overcome the No Show phobia.