[EM] Ranked Rankings (wasStrategic vs Dishonest)

Forest Simmons forest.simmons21 at gmail.com
Wed Sep 22 18:48:01 PDT 2021

```Ballots are ordinal rankings with equal rankings, truncations, and relative
strength of rankings enabled.

A>B>>>>C>>D=E>F>>>G for example is an allowed ballot expressing preferences

intensity of the preferences ...
the preference A>B is not as intense as C>>D, for example.  Is it supposed
to be half as intense? No, just less intense.

Does B>>>>C on one ballot mean more than B>>C on another ballot? No, the
intensity comparisons have meaning only within ballots.

Here's an example of a method that makes use of this kind of information:

Let X and Y be the two candidates that (for the greatest number of ballots)
find themselves on opposite sides of a preference when only the max
intensity preferences of each ballot are not suppressed.

Then let BX and BY be the respective subsets of ballots that prefer X over
Y and vice-versa.

method applied recursively to BX and BY.

I'm sure you can think of better versions of this basic idea!

El lun., 20 de sep. de 2021 6:20 p. m., Forest Simmons <
forest.simmons21 at gmail.com> escribió:

> Very thoughtful insights!
>
> Something you said reminds me that there is a ballot type that requires
> only ordinal information ... no utilities, but is much more expressive than
> Universal Domain allows .... because the order is not just a ranking of the
> candidates but an order of the intensities of preference.
>
> The first time I heard of Ranked Pairs before reading further I thought
> "Great idea, let the voters rank the pairwise preferences in order of
> perceived importance!"
>
> This can be expressed by augmenting inequality symbols with more chevrons
> to indicate relative strength of preference:
>
> A>B>C>D becomes A>>B>C>>>D, for example.
>
> How to make good use of the second order ordinal information contained in
> these ranked rankings is fun to contemplate!
>
> Not likely to be a public proposal any time soon, unless VPR becomes
> popular ... then we could have VPRR, vote for a public ranked ranking.
>
> El lun., 20 de sep. de 2021 3:52 p. m., Kristofer Munsterhjelm <
> km_elmet at t-online.de> escribió:
>
>> On 9/20/21 8:55 PM, Forest Simmons wrote:
>> > I know this is picky semantics to some people, but to me strategic
>> > voting does not imply dishonest voting.
>>
>> Some ideas of how to formalize my three levels:
>>
>> Suppose that there exists a "reference method" where optimal behavior
>> coincides with what we would consider honest, and that thus under
>> honesty fixes some parameters of the ballot. (E.g. Random Ballot for
>> Plurality, Random Pair for Condorcet matrices and full ranked ballots,
>> and Hay for linear/affine scalings of utilities.)
>>
>> Then level one behavior is only strictly speaking possible in a method
>> that has no free parameters once the fixed parameters are set according
>> to the reference method: level one is just voting the way the reference
>> method incentivizes. (Alternatively: if there are free parameters left
>> over, choosing them in a way that doesn't depend on what candidates are
>> running.)
>>
>> Level two is possible in a method that has free parameters left over
>> once we're constrained to honest behavior over the (now fixed)
>> parameters. E.g how to equal-rank or truncate (but not reverse
>> preferences) in a method that allows for equal-rank or truncation; what
>> linear (or affine) transformation to use when rendering utilities into
>> Range scores; and where to put the Approval cutoff. Engaging in level
>> two behavior is either setting these free parameters, (or if you chose
>> the alternative definition above: setting them in a way that depends on
>> who's running.)
>>
>> Level three is simply voting differently for the fixed parameters, i.e.
>> not voting the ballot that you would under the reference method.
>> (Preference reversal, etc.)
>>
>> The problem with this rough idea is that there's no way to delineate
>> things so that equal-rank and truncation is honest (level one) while
>> approval cutoff decisions are level two. The closest I can think of is
>> to say that equal-rank is level one if it's done in a way that's
>> independent of irrelevant candidates (e.g. I rank down to when I feel
>> tired, or I equal-rank everyone who's some epsilon away from each other
>> by utility). That's the alternative definition above.
>>
>> But I suspect that the levels are also about intent... and there's also
>> something else (I don't know if it's the high stakes or some artificial
>> aspect to being asked to boil everything down to yes or no) that makes
>> approval much harder to decide than equal-rank.
>>
>> Just some thoughts :-)
>>
>
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