Quantile-Normalized Score
-
@jack-waugh if q is a real number in [0,1], a q-quantile of a random variable X is a value x such that Prob(X<=x)=q. For example, a median is a 0.5-quantile (aka 50th percentile).
I don’t really care for StatQuest, since I find it to be fairly patronizing… but here’s this: https://youtu.be/ecjN6Xpv6SE?si=XGugEzrGvUX078VF
-
This post is deleted! -
@jack-waugh I doubt it. But I'm still not sold that Frohnmayer balance is either meaningful or desirable. At the heart of the criterion is cancellation, which treats the election in some sense as a zero-sum game. I don't think it's necessary to do that.
-
@cfrank said in Quantile-Normalized Score:
not sold that Frohnmayer balance is either meaningful or desirable
Do you object to Choose-one Plurality for a single winner? On what grounds?
-
@jack-waugh I surely do! The main reason I object is that voters intrinsically suffer from untenable conflicts of interest when casting their ballots. This is also inextricably tied to the consequences of the system and its failure to satisfy independence of clones in particular, leading to the formation of a political duopoly wherein those exact conflicts of interest presented to voters via the character of the “choose-one” ballot structure are, passively or otherwise, exploited to enable the propping up of arbitrary, parasitic, pseudo-democratic power structures that ultimately have, often not without intention, minimized within unavoidable constraints their accountability to the electorate.
While I do think that there needs to be a degree of balance in a reasonable electoral system, I don’t think that Frohnmayer’s formalization of balance actually means what it intends to, or even that it is always well-defined.
-
@cfrank So it looks as though you have two main lines of reasoning in opposing choose-one plurality, and they start with, respectively:
-
conflicts of interest experienced by the voters;
-
dependence on clone candidates.
How can we observe or reason that voters face conflicts of interest? Is this about each voter individually, or about some aggregates from among them? What is the conflict, and how does it cause a problem? Do alternative voting systems take away the conflict of interest? How?
-
-
@jack-waugh essentially, there can never be a total removal of conflicting interests, which is more or less a consequence of Gibbard’s theorem. People strategize only to navigate conflicts of interest. In choose-one voting, the conflict of interest is manifest in spoiler candidates and choosing the “lesser of evils” candidate, or a popular candidate, rather than the candidate a voter would actually hope to win the election. In my mind, the goal is, roughly, to find a way to minimize these conflicts while preserving choice, even including conflicts regarding issues of participation and ballot complexity.
The way I think of to reason about conflicting interests is to consider oneself as a generic voter and to conceptualize the task of making a decision on how to vote in relevant circumstances in order to achieve various goals. When there are clear, significant goals that require incompatible solutions, that introduces a conflict of interest. Obviously a choice of A versus B must be made somewhere, but the question is one of the needless frequency and severity of certain conflicts that can otherwise be mitigated by adopting a system that is superior in that regard.
I think the fact that “choose-one” is rated so low in all of our little tags here is an indication that we can easily see when conflicting interests are too frequent and severe to be tenable when reasonable alternatives exist. This is a pretty philosophical topic and I’m not confident there will ever be a clear answer. But one thing is for sure: failing independence of clones opens up a significant dimension to be populated with conflicting interests.
-
@cfrank said in Quantile-Normalized Score:
minimize these conflicts
If it's possible to minimize the conflicts, that implies some sort of measure for how severe the conflict is. What do you want to minimize, mathematically?
-
@jack-waugh I don’t think it’s a simple mathematical problem. Math can help, but only after a model is chosen, and I can’t claim to know what the correct model should be. I see it as a philosophical problem, and my approach to it is fully consequentialist, where formal theory is only a concern to me as a proxy.
What I mean is that to me, the core of the problem is in the domain of continental philosophy, with analytical philosophy as a secondary supplement.
After a brief chat with ChatGPT, here is how it categorized the philosophical disposition I call “social consequentialism”:
‘’’
Classification
Ethical Foundation: Rooted in consequentialism, with an emphasis on the outcomes of actions but uniquely focused on social consequences.
Philosophical Tradition: A fusion between analytic and continental traditions, using analytic clarity and rigor to address the broad, context-sensitive concerns typical of continental philosophy.
Social and Political Philosophy: Places a strong emphasis on the social implications of actions, potentially aligning with theories of social justice, communitarianism, and democratic ethics.
Questions for Deeper Understanding
Scope of Social Consequences: How do you define or delimit "social consequences"? Are there specific aspects of social life (e.g., justice, equality, freedom) that are prioritized in your assessment of outcomes?
Methodology for Assessing Outcomes: How do you propose to assess or measure the desirability of social consequences? What methodologies or criteria are used to evaluate the complex outcomes of actions on society?
Handling Conflicts and Trade-offs: How does social consequentialism navigate conflicts between individual and social outcomes, or between different social goods (e.g., equity vs. efficiency)?
Theoretical Influences and Precedents: Are there specific philosophers, theories, or movements within continental or analytic traditions that particularly influence your thinking? How do you position your theory in relation to utilitarianism, social contract theory, or critical theory?
Practical Implications and Applications: What are the practical implications of social consequentialism for policymaking, social activism, or individual ethical decision-making? How does it inform actions in concrete scenarios?
Temporal and Cultural Context: How does social consequentialism account for the variability of ethical judgments across different cultural contexts and historical periods?
‘’’
I thought the classification was pretty decent and also found the questions pretty central.
-
@cfrank said in Quantile-Normalized Score:
failure to satisfy independence of clones
What are the grounds to understand this as a problem?
-
@jack-waugh the grounds by which to say that failure of independence of clones is a problem is the collection of negative and avoidable social consequences it leads to. We have to agree on a state of affairs for us to recognize the same problems. For example, I think we both agree that political divisiveness, externally imposed conflicts of interest on the public, lack of accountability of public officials to the public, and all associated corruptions and abuses of power are problems, don’t we?
There is a delineated complex of issues that contribute to this vicious cycle, one of which is vote splitting, which is a simple consequence of the failure for clones to be independent. In contrast, I know of no clearly delineated complex of negative consequences that involves Frohnmayer’s formalization of balance. If you can identify a complex for me that stands up to scrutiny, I would be more convinced. But the state of it to me is that Frohnmayer balance appears to be a purely theoretical, arbitrary formalism with no clear tangible consequences, and therefore that using it as a criterion by which to judge the merit of voting systems is a fallacy.
-
@cfrank, under the conditions that I am peppering you with questions, I obviously have an obligation, as someone who would be seen as honest and fair in discourse, to at least try to answer the questions that you put to me in the discussion.
Do I agree that divisiveness is a problem? Let me take an example. There is division of opinion among US citizens in that some support genocide and others oppose it. If the condition were such that all supported genocide, the division would be gone, but the situation would be worse relative to my values. As I see it, the ideal situation would be that all the citizens oppose genocide, and the worst situation would be that all support it, and the divisive situation where some oppose it and others support it, is at an intermediate level of quality between the two extremes. This example illustrates why I do not agree that divisiveness is a problem. Division happens because people disagree about what is right and wrong and about what is desirable.
Do I agree that externally-imposed conflicts of interest on the public constitute problems? Yes. When AIPAC provides money support to candidates who support genocide, that is a conflict of interest with the needs of the citizens of the US such as food, clothing, and shelter, so that is an externally-imposed conflict of interest, and I do agree that that is a problem.
I agree that lack of accountability and the associated corruptions and abuses of power are problems.
What is the mechanism whereby failure of independence of clones leads to social consequences?
Please evaluate the following systems as to their acceptability or desirability relative to one another:
-
system 0: Approval Voting;
-
system 1: There is no "system 1" mentioned in this discussion.
-
system 2: The tally is as in Approval, but you are constrained to approve strictly fewer than half the count of candidates, unless there are only two. So for example, if six candidates are running, you can approve one or two, but not three or more, because three is not strictly less than half of six.
-
system 3: The tally is as in Approval, but you are required to approve strictly more-count than half the count of candidates, unless there are only two.
-
system 4: Choose-one Plurality.
-
system 5: You are required to approve all but one of the candidates.
-
-
@jack-waugh you’re right that divisiveness is not a problem in itself, but I suppose what I mean is that discourse is focused on issues that are divisive rather than on issues that can be addressed with a reasonable measure of consensus, and the controversial issues hold the reigns of policy rather than the agreements that exist.
And also, if everyone agrees that genocide is desirable, including the race of people who would be exterminated, we enter a pretty absurd and peculiar ethical territory. The agreement you’re talking about presupposes a disenfranchisement of a group of people, which itself goes against the preservation of liberty and choice and natural rights. It’s complicated and there may be strong arguments that are concise, but I won’t try to make any because more likely it would have glaring objections. On the whole and sophistry aside (by that I refer to my own sophistry), I think we agree. I’ll think about your points.
-
@cfrank Can you explicitly explain this method, rather than making us infer it from a related Wikipedia article?
-
@toby-pereira yes sorry! There was an explanatory video I shared with @Jack-Waugh, I just put it at the top next to the Wikipedia link, also here: Youtube Video
What’s sort of interesting about this is that there is no need for even a set scale, in principle people could put whatever scores they like, even negative numbers, and the normalization would still put everybody on the same scale and footing.
This kind of normalization is really common in computational biology to correct for batch effects and outliers, for example when trying to infer highly expressed genes in one sample of cells relative to another based on count data from RNA sequencing.
I’m running a small toy election about GitHub icons with my lab-mates, and comparing score to quantile normalized score, I like it. I’ve just been asking ChatGPT to quantile normalize and it does so successfully, but there are definitely more guaranteed, readily accessible methods that do this normalization efficiently even for huge data sets like an actual state or national election.
-
@cfrank Cool, thanks for that. My previous message was probably a bit blunter than I intended it to come across.
As a voting method I'm not sure it seems ideal to me, as it comes across a bit Borda-county. If there are e.g. 4 candidates, then regardless of whether one person scores them 10, 9, 1, 0 and another scores them 7, 6, 5, 4 they will be normalised to e.g. 8, 6, 4, 2 (or whatever the normalised values end up being). So it seems it will have all the problems Borda has, including failure of independence of clones.
Also, a voter might think the actual scores they give matter little because the distribution will be set by the whole population of which they are just a tiny proportion. That might make the scores even more like the Borda count as they just separate each candidate by 1 to make it easier.
How does it handle equal scores? Give them the mean of the scores they would occupy?
-
@toby-pereira yes it can handle equal scores. There’s a slight peculiarity in terms of discreteness of distributions, but equal scores will stay equal after the normalization, since they have the same quantile.
I agree that it’s Borda-like, but I think there’s a difference between set scores at the outset and scores that adjust depending on the ballots. I understand your concerns, and what the resolution to the questions you have might be isn’t wholly obvious to me at the moment. I think the only way to comprehend the differences is to do an actual results comparison over different ballot sets, for example, between this method and Borda and score. My guess is that they’ll be fairly different, but I could be wrong, and there might be weird effects of the normalization that I don’t see immediately.
In terms of scores not mattering, this is a makeshift idea, but if a score range is fixed, and if something like pseudo candidates (who cannot win) are entered with all minimum and all maximum scores for every voter, it is still advantageous for a voter to utilize the whole range to maximize the expressiveness of their ballot, which eliminates some of the arbitrary nature of selecting scores.
-
Do you agree that it is possible for two voters to have directly opposed positions on the candidates, such that each of the two voters hates the candidates the other one loves, and loves the candidates the other one hates?
-
@jack-waugh yes of course I do, but there isn’t any particular mathematical formalism naturally associated with that situation.
-
@cfrank Then how can you justify giving one of these voters more power to sway the outcome than you give to the other voter?