Beyond Condorcet: optimal aggregation rules using voting records

Baharad, Eyal; Goldberger, Jacob; Koppel, Moshe; Nitzan, Shmuel

doi:10.1007/s11238-010-9240-5

Cited by 11 publications

(4 citation statements)

References 25 publications

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“…were the 'correct' ones, we can determine, for any individual voter and to high precision, how likely he is to choose correctly this time around. We do so through a process called 'Q', developed by Baharad et al (2011Baharad et al ( , 2012 We would seem justified in taking a dim view of Smith's competence as a result of what we know about his choice in the first election and that election's overall result. There is, ex hypothesi, a truth of the matter about whether A or B is correct, and Smith's judgement was contradicted by the independent judgements of 120 million other people.…”

Section: The Application Of Theory To Politicsmentioning

confidence: 99%

Plural Voting for the Twenty-First Century

Mulligan

2017

The Philosophical Quarterly

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Recent political developments cast doubt on the wisdom of democratic decisionmaking. Brexit, the Colombian people's (initial) rejection of peace with the FARC, and the election of Donald Trump suggest that the time is right to explore alternatives to democracy. In this essay, I describe and defend the epistocratic system of government which is, given current theoretical and empirical knowledge, most likely to produce optimal political outcomes-or at least better outcomes than democracy produces. To wit, we should expand the suffrage as wide as possible and weight citizens' votes in accordance with their competence. As it turns out, the optimal system is closely related to J. S. Mill's plural voting proposal. I also explain how voters' competences can be precisely determined, without reference to an objective standard of correctness and without generating invidious comparisons between voters.

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Section: The Application Of Theory To Politicsmentioning

confidence: 99%

Plural Voting for the Twenty-First Century

Mulligan

2017

The Philosophical Quarterly

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“…There are various ways to model partial knowledge of expert competences (Baharad et al, 2011(Baharad et al, , 2012. Perhaps the simplest scenario for estimating the p i s is to assume that the i th expert has been queried independently m i times, out of which he gave the correct prediction k i times.…”

Section: Unknown Competences: Frequentist Approachmentioning

confidence: 99%

Consistency of weighted majority votes

Berend¹,

Kontorovich²

2013

Preprint

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We revisit the classical decision-theoretic problem of weighted expert voting from a statistical learning perspective. In particular, we examine the consistency (both asymptotic and finitary) of the optimal Nitzan-Paroush weighted majority and related rules. In the case of known expert competence levels, we give sharp error estimates for the optimal rule. When the competence levels are unknown, they must be empirically estimated. We provide frequentist and Bayesian analyses for this situation. Some of our proof techniques are non-standard and may be of independent interest. The bounds we derive are nearly optimal, and several challenging open problems are posed. Experimental results are provided to illustrate the theory.

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“…For a binary-choice problem with one correct and one wrong choice, the law of large numbers has mathematically explained the reason behind the higher accuracy of a majority vote compared to an individual's decision-making [2,[16][17][18][19][20]. Theoretical studies have also revealed that the optimum weight to be given to opinions to maximise the majority vote accuracy is proportional to the log-odds ratio of the individual's ability [17,18,21].…”

Section: Introductionmentioning

confidence: 99%

Casting votes of antecedents play a key role in successful sequential decision-making

Ito

Sasaki²

2023

PLoS ONE

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Aggregation of opinions often results in high decision-making accuracy, owing to the collective intelligence effect. Studies on group decisions have examined the optimum weights for opinion aggregation to maximise accuracy. In addition to the optimum weights of opinions, the impact of the correlation among opinions on collective intelligence is a major issue in collective decision-making. We investigated how individuals should weigh the opinions of others and their own to maximise their accuracy in sequential decision-making. In our sequential decision-making model, each person makes a primary choice, observes his/her predecessors’ opinions, and makes a final choice, which results in the person’s answer correlating with those of others. We developed an algorithm to find casting voters whose primary choices are determinative of their answers and revealed that decision accuracy is maximised by considering only the abilities of the preceding casting voters. We also found that for individuals with heterogeneous abilities, the order of decision-making has a significant impact on the correlation between their answers and their accuracies. This could lead to a counter-intuitive phenomenon whereby, in sequential decision-making, respondents are, on average, more accurate when less reliable individuals answer earlier and more reliable individuals answer later.

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Beyond Condorcet: optimal aggregation rules using voting records

Cited by 11 publications

References 25 publications

Plural Voting for the Twenty-First Century

Plural Voting for the Twenty-First Century

Consistency of weighted majority votes

Casting votes of antecedents play a key role in successful sequential decision-making

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