[EM] approval cutoff ballot possibilities

[Ted Stern]

I notice there are several explicit approval cutoff methods being discussed
on the list.

Kevin Venzke has suggested a number of rank-flattening proposals, with
Chris Benham proposing a simplified version of one of them:
Condorcet-using-full-preferences // Condorcet-using-approved-preferences //
Approval.  The latter can be used to handle Forest Simmon's 3 approval
cutoff examples.  I like this method due to its relative simplicity and
self consistency.  I propose calling this it Instant Round Robin Rank
Flattened Fallback, or IR3F2.

Whichever approval cutoff method one uses, there is some latitude in how
one could implement an explicit approval cutoff.

I've been thinking about 6, 7 or 10 slot methods, with an explicit
Disapproval Level added as a candidate (any candidate rated at DL or below
is disapproved).  If the default rate is lowest rate, then it makes sense
for DL to be an extra "candidate", with the same default.  Then approval is
any rate above that given to DL.  Using this form, a voter who doesn't
exercise their option to reset the Disapproval Level is basically using
implicit approval cutoff at rate 0.

Having an extra DL candidate also enables the opportunity for a voter to
disapprove every candidate by voting DL at top rate, which I could see
people doing as some form of None-of-the-above protest.  I dimly recall
something of this sort being discussed a few years back.

When I am able to chat about this with my 18yo son as a captive audience
(e.g. last night while building IKEA furniture together), he seems to like
ranks 1 through 10, and can follow the rank flattening logic just fine, but
thinks that it would be a challenge for
 most voters to understand the Condorcet method itself, let alone the rank
flattening.  Granted, this is a sample size of one :-).

One issue with doing pairwise comparisons with flattening is the
requirement to store 2 different arrays.  Is there any way to use the extra
DL candidate's pairwise scores to infer the amount that needs to be
modified in the normal full-preference pairwise array?  If not, what if
there were a minimum-approval candidate instead?
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