I am interested in voting theory, but I wouldn’t say I have deep knowledge about it, so things starting at the paragraph “The typical framework for the analysis of multiperiod voting is the “independent identically distributed” (i.i.d) setting” are completely new to me.
I found SV-PAYW and the Karma System to be understandable at a high level, but the paragraph about Quadratically Normalized Utilitarian Voting feels underspecified, like I kind of understand what it does, but ~0 about how it works except in its name.
Also, your title “Arrow theorem is an artifact of ordinal preferences” feels very disconnected from the actual content. My blind expectation is an essay that gives intuition about why the Arrow Theorem is true as some obvious-after-you-explained-it consequences of ordinal preference style voting, not a literature review.
Judging from the content alone I find it enjoyable to read and flows nicely, but a bit terse. Expected level of terseness for a paper though.
“The typical framework for the analysis of multiperiod voting is the “independent identically distributed””
In the i.i.d framework, what happens in a period stays in that period. That is, you vote, the outcome happens, it influences your utility in the period, but the possible outcomes in (t+1) does not depend in the outcomes in the period t. Another way to say this, is that the only “memory variable” in any period is the votes endowment at the end of period. With “path dependence” (beyond vote endowments), dynamic voting theory is too dynamic...
Arrow is too complex to be discussed here, while the short explanation here (you cannot turn N ordinal preferences into a “social ordinal preference” for a group) is in my view captures the most important meassage. Any general mechanism to turn a group of ordinal preferences into a social preference is susceptible of creating paradoxical results. On the other hand, Dhillon & Mertens Relative Utilitarianism shows this is not the case for turning individual cardinal preferences into social ones[at least for a finite number of possible outcomes]. It is a little bit puzzling that this is not the standard intepretation, and that is why I wrote this.
I am interested in voting theory, but I wouldn’t say I have deep knowledge about it, so things starting at the paragraph “The typical framework for the analysis of multiperiod voting is the “independent identically distributed” (i.i.d) setting” are completely new to me.
I found SV-PAYW and the Karma System to be understandable at a high level, but the paragraph about Quadratically Normalized Utilitarian Voting feels underspecified, like I kind of understand what it does, but ~0 about how it works except in its name.
Also, your title “Arrow theorem is an artifact of ordinal preferences” feels very disconnected from the actual content. My blind expectation is an essay that gives intuition about why the Arrow Theorem is true as some obvious-after-you-explained-it consequences of ordinal preference style voting, not a literature review.
Judging from the content alone I find it enjoyable to read and flows nicely, but a bit terse. Expected level of terseness for a paper though.
“The typical framework for the analysis of multiperiod voting is the “independent identically distributed””
In the i.i.d framework, what happens in a period stays in that period. That is, you vote, the outcome happens, it influences your utility in the period, but the possible outcomes in (t+1) does not depend in the outcomes in the period t. Another way to say this, is that the only “memory variable” in any period is the votes endowment at the end of period. With “path dependence” (beyond vote endowments), dynamic voting theory is too dynamic...
Arrow is too complex to be discussed here, while the short explanation here (you cannot turn N ordinal preferences into a “social ordinal preference” for a group) is in my view captures the most important meassage. Any general mechanism to turn a group of ordinal preferences into a social preference is susceptible of creating paradoxical results. On the other hand, Dhillon & Mertens Relative Utilitarianism shows this is not the case for turning individual cardinal preferences into social ones[at least for a finite number of possible outcomes]. It is a little bit puzzling that this is not the standard intepretation, and that is why I wrote this.
Thank you for your interest!