Voting by Compendium

This is a philosophical idea that is probably impractical, but also seems like it would address a variety of concerns about fairness and the translation of ballots into aggregate voter preferences.
Suppose that the ballots take a format where the similarity of any two aggregations of ballots can be determined according to a welldefined "discriminant" function. A compendium of samples of aggregate ballots with arbitrary candidate labels could in principle be produced, along with an agreedupon or accepted definition of the winner or the set of winners for each sample. These definitions of the winner could be determined themselves by a prior electoral process.
For any aggregation of ballots, then, one could simply compute the sample in the compendium that is most similar, and then determine the winner or winners accordingly.

Can't say I understand your verbiage. Maybe if you translate it to math ...

@jackwaugh I gotchya, unfortunately the issue is that I am trying to remove much of the mathematics
What I mean is that rather than try to simplify the voting rules into a highly compressed algorithm, why not lay out an easilynavigable compendium of predefined, agreed upon casebycase rules? Like a legal document, for example, stating things like, â€śIf the ballot set is most near to example X, then our compendium determines that candidate A is to have won the election.â€ť
Like I said this is theoretical and not practical per se, which is why this is in the philosophy section. The benefit of having such a compendium is that it more or less would detail every possible outcome of any election up front, as â€śaxiomsâ€ť rather than â€śtheorems.â€ť This way, the end results of elections do not rely on applying general rules to arrive at conclusions, but rather the conclusions themselves are the objects under consideration.

It's possible to change notations, but any deterministic procedure is fundamentally applied math. Do you want to bring a committee of electoral judges to make a subjective determination given the votes and the compendium?

@cfrank said in Voting by Compendium:
What I mean is that rather than try to simplify the voting rules into a highly compressed algorithm, why not lay out an easilynavigable compendium of predefined, agreed upon casebycase rules? Like a legal document, for example, stating things like, â€śIf the ballot set is most near to example X, then our compendium determines that candidate A is to have won the election.â€ť
Could you maybe give an example of how this might work? Ballot sets are quite complex, and it certainly won't be as simple as having a dozen example ballot sets and then deciding which of these sets the real ballot set is nearest to.

@tobypereira this is precisely what I mean. If there is an agreed upon mathematical function that computes the discriminant between two ballot sets, and if the examples in the compendium are diverse enough to populate the space of ballot sets to sufficient density, then it does become that simple. A dozen examples may not be sufficient, but there may be a number or set of examples that is both tractable and functionally sufficient.

@cfrank said in Voting by Compendium:
Suppose that the ballots take a format where the similarity of any two aggregations of ballots can be determined according to a welldefined "discriminant" function.
Please lay out such a format and function.

@jackwaugh an example could be ballots as elements of a vector space whose basis consists of all rankings of candidates. For instance,
abc+bca+cab
as well as
acb+cba+bac
represent (oppositely oriented) Condorcet cycles.
Ballot sets could be normalized to have a sum of coefficients of +1, and a metric can be defined over this space in many ways, including a simple Euclidean distance, or a Wasserstein distance.

OK, that's starting to sound concrete. Are you going to sum up the vectors indicated by the cast ballots and sum those in each entry in the compendium and apply the distance measure between the sums and choose the winner indicated by the closest entry? Shall there have to be a compendium for each count of candidates that the technique can accept?

@jackwaugh Iâ€™m imagining a compendium thatâ€™s populated densely enough with examples that it suffices for all practical purposes

I get that, but reducing a collection of real or hypothetical votes to their sum throws away a lot of information. And I don't know a proof that the information thrown away is unimportant for our purposes. Maybe it is, but I don't know.

@jackwaugh in the space Iâ€™m considering above as an example, a ballot set like
10abc+7bcd+2acd
is just a representation for
10: a>b>c>d
7: b>c>d>a
2: a>c>d>bso no information is thrown away. The letters are candidates and the product terms like â€śabcâ€ť and â€śacdâ€ť represent rankings of candidates, so the â€śproductâ€ť here between candidates to produce rankings is not commutative.
You can also represent score ballot sets as polynomials. For example,
5 a^5 b^4 c^1 + 2 a^1 b^5
could represent a score ballot set of
5: a[5] b[4] c[1] d[0]
2: a[1] b[5] c[0] d[0]and the product could be commutative.
And happy Thanksgiving!

Ballot sets could be normalized to have a sum of coefficients of +1, and a metric can be defined over this space in many ways, including a simple Euclidean distance, or a Wasserstein distance.
To what arguments will you apply the distance measure?
And as for the day of the year, please join me in mourning for Indigenous victims of genocide as well as those in Palestine. Now someone will say I went off topic and should have to apologize or get kicked out, but I did not initiate the foray into the meaning of the day. And someone who promotes a political or social position can expect a response from adherents of the other side, or multiple other sides.

@jackwaugh the position measure would essentially be determined by the probability distribution over the basis rankings, so it would be a discriminant measure between distributions.
I agree the past is full of tragedy, and every day of the year could easily commemorate some horrible thing. Some of them are excuses to take off work and see friends and family for a potluck

@cfrank, I don't know how to calculate a probability distribution over a collection of rankings. Maybe someone who knows statistics can understand your proposal and maybe critique it.
In regard to "tragedy", I judge that too broad a word, as it includes accidents, and "past", not fully accurate, because, among other reasons, Mr. Biden is killing children by the minute with US resources.
I ask you to join me in mourning the death of Layan Mohammed Sayed AlAker, who was two years old, a girl.
I ask you to join me in spending a minute and a few tears on Samir Mahmoud Hassan Abu AlHawa, who was a man, aged 62.
I received the suggestion to "hold space" from an organization, the "US Campaign for Palestinian Rights". Is this organization a grift? Yes, to an extent, they probably are, as indicated by the fact that they have an "executive director", which usually means a person drawing pay out of donations. Nevertheless, I judge the message of this organization more honest than the official story, which "happy Thanksgiving" ties into. This organization suggests for thingstaking day, among other practices (which I admit to not having followed):
When you gather with your loved ones, hold space for mourning the mass killing of Indigenous people from Turtle Island to Palestine. Hold a mourning ritual based in your communityâ€™s traditions. You may read the names and stories of our beloved people killed by colonial violence (for example, see here).
So I'm endorsing this organization's request, the one that I repeated above, in the context of your having wished me a happy Thanksgiving at this fraught time.