[EM] uses of truncation

[Forest W Simmons]

In my recent posting on this subject I mistakenly argued that if the 
truncation cutoff was uncovered, then it was also unbeaten.

It is convenient to treat the truncation cutoff as a virtual candidate, 
"trunc."

There are three cases to consider:

Case 1.  Trunc is the beats all candidate.

Case 2.  Trunc is uncovered, but not the beats all candidate.

Case 3.  Trunc is covered.

A "grand compromise," based on ordinal ballots with truncation allowed, 
could go something like this:

In case 1 take the D2MAC winner.

In case 2 take the candidate that beats trunc by the largest margin.

In case 3 use UncTrunc:  Initialize a list with trunc.  While no 
candidate on the list is uncovered, add to the top of the list that 
candidate (among the ones that cover the current top candidate T) who 
has the greatest number of winning votes against T.

Another possibility that I didn't mention in my previous message on 
this topic is this:

Let M represent any method that is based on ordinal ballots with 
truncation allowed and that has immunity to second place complaints.

Apply method M to the set of candidates augmented with the candidate 
trunc, i.e. trunc is to be treated like any other candidate.  If trunc 
is the method M winner, then elect the second place candidate.

If explicit approval is also allowed, then augment the set of 
candidates with both trunc and app (the approval cutoff).  [Since app 
Pareto dominates trunc, any method that satisfies IPDA could dispense 
with trunc.]  If app wins, then elect the second place winner.

Forest