The dependence of the majority voting decision-making probabilities on a multi-expert binary system experts number

2020 ◽  
pp. 7-14
Author(s):  
E. D. Avedyan ◽  
Le Thi Trang Linh
Keyword(s):  
Decision Making ◽  
Binary System ◽  
Conditional Probability ◽  
Majority Voting ◽  
Correct Solution ◽  
Conditional Probabilities ◽  
Analytical Results ◽  
Independent Expert ◽  
Mutually Independent

The article presents the analytical results of the decision-making by the majority voting algorithm (MVA). Particular attention is paid to the case of an even number of experts. The conditional probabilities of the MVA for two hypotheses are given for an even number of experts and their properties are investigated depending on the conditional probability of decision-making by independent experts of equal qualifications and on their number. An approach to calculating the probabilities of the correct solution of the MVA with unequal values of the conditional probabilities of accepting hypotheses of each statistically mutually independent expert is proposed. The findings are illustrated by numerical and graphical calculations.

Schließen mit Erfahrungssätzen

2021 ◽  
Author(s):  
Paola Janßen
Keyword(s):  
Decision Making ◽  
Research Unit ◽  
Prima Facie ◽  
Economic Research ◽  
Court Decisions ◽  
Applied Statistics ◽  
Conditional Probabilities ◽  
Empirical Methods ◽  
Legal Decision Making ◽  
The University

When dealing with experiential sentences in court, there is a risk of committing the probabilistic inverse fallacy, the swapping of conditional probabilities. Such a fallacy can be serious in legal decision making. Using empirical methods, the dissertation shows that this fallacy can be observed in civil procedural court decisions in which prima facie evidence is used and can have a significant impact on decision making. The dissertation was written at the Research Unit "Statistics in Court" of the Chair of Empirical Economic Research and Applied Statistics at the University of Bremen.

Costly Voting

2004 ◽  
Vol 94 (1) ◽  
pp. 57-66 ◽  
Author(s):  
Tilman Börgers
Keyword(s):  
Decision Making ◽  
Majority Voting ◽  
Voluntary Participation ◽  
Voting Rules ◽  
Value Model ◽  
Private Value ◽  
Two Alternatives ◽  
Costly Voting

What are good voting rules if voting is costly? We analyze this question for the case that an electorate chooses among two alternatives. In a symmetric private value model of voting we show that majority voting with voluntary participation Pareto-dominates majority voting with compulsory participation as well as random decision-making.

scholarly journals Quorums enable optimal pooling of independent judgements

2018 ◽  
Author(s):  
James Marshall ◽  
Ralf H.J.M. Kurvers ◽  
Jens Krause ◽  
Max Wolf
Keyword(s):  
Decision Making ◽  
Signal Detection ◽  
Signal Detection Theory ◽  
Detection Theory ◽  
Collective Decision ◽  
Majority Voting ◽  
Single Shot ◽  
Collective Decision Making ◽  
Trade Offs ◽  
Speed Accuracy

Majority-voting and the Condorcet Jury Theorem pervade thinking about collective decision-making. Thus, it is typically assumed that majority-voting is the best possible decision mechanism, and that scenarios exist where individually-weak decision-makers should not pool information. Condorcet and its applications implicitly assume that only one kind of error can be made, yet signal detection theory shows two kinds of errors exist, ‘false positives’ and ‘false negatives’. We apply signal detection theory to collective decision-making to show that majority voting is frequently sub-optimal, and can be optimally replaced by quorum decision-making. While quorums have been proposed to resolve within-group conflicts, or manage speed-accuracy trade-offs, our analysis applies to groups with aligned interests undertaking single-shot decisions. Our results help explain the ubiquity of quorum decision-making in nature, relate the use of sub- and super-majority quorums to decision ecology, and may inform the design of artificial decision-making systems.Impact StatementTheory typically assumes that majority voting is optimal; this is incorrect – majority voting is typically sub-optimal, and should be replaced by sub-majority or super-majority quorum voting. This helps explain the prevalence of quorum-sensing in even the simplest collective systems, such as bacterial communities.

Democracy in the Firm

2021 ◽  
pp. 38-59
Author(s):  
Hervé Crès ◽  
Mich Tvede
Keyword(s):  
Decision Making ◽  
Political Stability ◽  
Collective Decision ◽  
Majority Voting ◽  
Optimal Rate ◽  
Collective Decision Making ◽  
Market Failures ◽  
Democratic Principle ◽  
The Social ◽  
Decision Making Problem

The problem of collective decision-making arising from market failures is addressed using the democratic principle applied within the assembly of shareholders. A basic requirement is imposed (the Pareto principle): collective choices should not be at odds with the interests of all shareholders, as expressed by their preferences. This requirement puts bounds on what the collective can choose: it should remain within the set of averages of what the shareholders want. Further refining these bounds, a notion of political stability is proposed; it is defined with respect to (super) majority voting. One searches for the smallest rate of super majority for which a stable collective choice exists. This optimal rate is reviewed under classical assumptions from the social choice literature. It is shown how the dimensionality of the collective decision-making problem and the polarization of the electorate critically impact political stability, and hence the optimal rate of super majority.

scholarly journals NONCONGLOMERABILITY FOR COUNTABLY ADDITIVE MEASURES THAT ARE NOT κ-ADDITIVE

2016 ◽  
Vol 10 (2) ◽  
pp. 284-300 ◽  
Author(s):  
MARK J. SCHERVISH ◽  
TEDDY SEIDENFELD ◽  
JOSEPH B. KADANE
Keyword(s):  
Conditional Probability ◽  
Inaccessible Cardinal ◽  
Conditional Probabilities ◽  
Uncountable Cardinal ◽  
Additive Probability ◽  
De Finetti ◽  
Additive Measures

AbstractLet κ be an uncountable cardinal. Using the theory of conditional probability associated with de Finetti (1974) and Dubins (1975), subject to several structural assumptions for creating sufficiently many measurable sets, and assuming that κ is not a weakly inaccessible cardinal, we show that each probability that is not κ-additive has conditional probabilities that fail to be conglomerable in a partition of cardinality no greater than κ. This generalizes a result of Schervish, Seidenfeld, & Kadane (1984), which established that each finite but not countably additive probability has conditional probabilities that fail to be conglomerable in some countable partition.

Conditional Probability

2017 ◽  
Author(s):  
Kenny Easwaran
Keyword(s):  
Conditional Probability ◽  
Conditional Probabilities ◽  
Unconditional Probability

Conditional probability has been put to many uses in philosophy, and several proposals have been made regarding its relation to unconditional probability, especially in cases involving infinitely many alternatives that may have probability 0. This chapter briefly summarizes some of the literature connecting conditional probabilities to probabilities of conditionals and to Humphreys' Paradox for chances, and then investigates in greater depth the issues around probability 0. Approaches due to Popper, Rényi, and Kolmogorov are considered. Some of the limitations and alternative formulations of each are discussed, in particular the issues arising around the property of “conglomerability” and the idea that conditional probabilities may depend on a conditioning algebra rather than just an event.

scholarly journals Disintegration and Bayesian inversion via string diagrams

2019 ◽  
Vol 29 (7) ◽  
pp. 938-971 ◽  
Author(s):  
Kenta Cho ◽  
Bart Jacobs
Keyword(s):  
Probability Theory ◽  
Conditional Probability ◽  
Opposite Direction ◽  
Bayesian Inversion ◽  
Conditional Probabilities ◽  
Discrete Probability ◽  
Joint State

AbstractThe notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These notions exist in the literature, in concrete situations, but are presented here in abstract graphical formulations. The resulting abstract descriptions are used for proving basic results in conditional probability theory. The existence of disintegration and Bayesian inversion is discussed for discrete probability, and also for measure-theoretic probability – via standard Borel spaces and via likelihoods. Finally, the usefulness of disintegration and Bayesian inversion is illustrated in several examples.

scholarly journals N-gram probability effects in a cloze task

2014 ◽  
Vol 9 (3) ◽  
pp. 437-472 ◽  
Author(s):  
Cyrus Shaoul ◽  
R. Harald Baayen ◽  
Chris F. Westbury
Keyword(s):  
Conditional Probability ◽  
Language Processing ◽  
Implicit Knowledge ◽  
Empirical Measure ◽  
Word Choice ◽  
Conditional Probabilities ◽  
Linguistic Context ◽  
Specific Context ◽  
Probabilistic Information ◽  
N Gram

What knowledge influences our choice of words when we write or speak? Predicting which word a person will produce next is not easy, even when the linguistic context is known. One task that has been used to assess context dependent word choice is the fill-in-the-blank task, also called the cloze task. The cloze probability of specific context is an empirical measure found by asking many people to fill in the blank. In this paper we harness the power of large corpora to look at the influence of corpus-derived probabilistic information from a word’s micro-context on word choice. We asked young adults to complete short phrases called n-grams with up to 20 responses per phrase. The probability of the responded word and the conditional probability of the response given the context were predictive of the frequency with which each response was produced. Furthermore the order in which the participants generated multiple completions of the same context was predicted by the conditional probability as well. These results suggest that word choice in cloze tasks taps into implicit knowledge of a person’s past experience with that word in various contexts. Furthermore, the importance of n-gram conditional probabilities in our analysis is further evidence of implicit knowledge about multi-word sequences and support theories of language processing that involve anticipating or predicting based on context.

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