[EM] EXACT, a Majority Judgment-like IBIFA variant w/FBC and IBI

[Kristofer Munsterhjelm]

On 12/26/2017 12:43 AM, Ted Stern wrote:
> Chris Benham proposed IBIFA in May and June, 2010, on the
> election-methods mailing list:
>
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2010-May/091807.html
> <http://lists.electorama.com/pipermail/election-methods-electorama.com/2010-May/091807.html>
>
> http://election-methods.electorama.narkive.com/KdBxpweB/irrelevant-ballots-independent-fallback-approval-ibifa
> <http://election-methods.electorama.narkive.com/KdBxpweB/irrelevant-ballots-independent-fallback-approval-ibifa>
>
> http://wiki.electorama.com/wiki/IBIFA
> <http://wiki.electorama.com/wiki/IBIFA>
>
> IBIFA is, as originally stated, a "Bucklin-like method meeting Favorite
> Betrayal and Irrelevant Ballots."  Its key principle is to compare the
> ballots voting for a candidate at-or-above a particular rating to the
> most-approved candidate on the complementary ballots.  When the former
> exceeds the latter, a meaningful threshold has been crossed, unlike the
> arbitrary 50% threshold of median rating methods.  This is what enables
> IBIFA to yield the same result if irrelevant ballots are added or
> dropped.  By construction, IBIFA is cloneproof.
>
> With this in mind, I realized that a minor modification of IBIFA would
> make it more like Majority Judgment, reducing later-harm and improving
> Condorcet consistency (though not completely), while satisfying the same
> criteria as MJ.

Do you think it's possible to generalize that strategy to handle 
multiwinner elections as well? I can't see any obvious ways, but it 
would be nice if one could make multiwinner methods with implicit 
thresholds as well, since the vast majority uses explicit thresholds 
(usually the Droop quota).

> EXACT does require several N^2 arrays for summable storage, but note
> that no sorting of the ballots is required as with pairwise methods.

Pairwise methods don't strictly require that ballots are sorted. E.g. 
the following will produce a Condorcet matrix (if there's no truncation 
or equal rank):

for i = 1 to num ballots
	for j = 1 to num candidates
		c1 = candidate ranked at jth place on the ith ballot

		for k = j+1 to num candidates
			c2 = candidate ranked at kth place on the ith ballot
			matrix[c1 beats c2] += weight of ballot i

It's a bit of a nitpick, though :-)