[EM] HBH

[fsimmons at pcc.edu]

> From: Kevin Venzke 
> Hi Forest,
> 
> So here's my summary using a 4-slot ballot and 3 candidates 
> let's say.
> 
> The "pecking order" is the Range order. Assume no ties.

I suppose that you could use the range order for the pecking order, but as you mention below that could 
lead to some strategic distortions.

The pecking order I had in mind is more like implicit approval; if implicit approval (number of above zero 
ratings) has no ties, that's all it is.

> 
> The "proximity" between two candidates is the smaller of 6 
> (3*2), and 
> the product of the two candidates' ratings, summed from each ballot.
> 
> When finding the nearest candidate to another specific candidate,
> break ties such that higher pecking order placement means one is 
> closer.(Assuming, I suppose, that a higher-order candidate wants 
> to go later.)
> 
> Pairwise contests are determined by majority wins if available. 
> Otherwise the pecking order winner wins.
> 
> You start the method with V = the Range loser generally. Call 
> him "C."
> Find the most distant candidate from C, call him "B." Eliminate the
> loser of the pairwise contest (according to the above 
> paragraph), which
> leaves you with either B or C to compare to A, who is by default the
> furthest candidate from whoever is left.

Right!

> 
> I understand the Plurality argument. Still wrapping my head 
> around the
> monotonicity and compromise ones. 

The key to montonicity is that from the first time the eventual winner becomes the defending champ, she 
has to defeat every challenger, i.e. all of the remaining candidates.  So if a winner W gets barely enough 
increased support to change the proximity order by just one pair, say W is now closer to V, than W' 
instead of vice-versa, then W' challenges V before W.  Whether or not W' or the current V weathers this 
challenge doesn't matter, because W beat the current V before, and then beat W' and all of the other 
remaining candidates later.

If the winner gets lots of increased support, just gradually add that support so that it makes this minimal 
change in the order, and note that each time this kind of minimal change is made, the winner stays the 
same.  If we wanted to get fancy, we would call this a homotopy argument.

>I get what the latter mechanic 
> is 
> doing, I just wonder if it can really be that easy?

Well, it could be that voter Joe is the only one that thinks that his compromise is a good compromise for 
his favorite, so that they don't end up with high proximity after all.   If he doesn't realize this, he won't 
have any incentive to compromise.  If he does realize it, then he may well have significant incentive to 
compromise.  But most voters are not going to be confused about who the natural compromise 
candidates are for their favorites, and this agreement will ensure that they have high proximity, i.e. most 
voters will not find their compromise pitted against their favorite unless they both survive until very late in 
the game.

> 
> Strategy-wise I am a bit concerned that your raw Range score is going
> to be important more often.
> 
> I'll implement it when I get a moment.
> 
> Kevin