More jury theorems

[rmaniv]

Expand the theorems package with the following models (from Wikipedia):

Correlated votes

• Growing infallibility might not hold if votes are correlated (weakening the unconditional independence claim). https://doi.org/10.1007%2Fs11238-009-9170-2
• Growing reliability and crowd infallibility hold under conditional independence, competence and uniformity. https://plato.stanford.edu/entries/jury-theorems/#PartSoluCondJuryTheo
• Crowd infallibility holds if the probability of following the opinion leader is less than 1-1/2p (where p is the competence level of all voters). https://doi.org/10.2307%2F3214318
• Growing reliability holds but the asymptote is below a probability of 1 under conditional independence, "tendency to competence," and conditional uniformity. Tendency to competence: "for each voter, and for each r>0, the probability that p(x) = 1/2+r is at least as large as the probability that p(x) = 1/2-r." (from wiki) https://doi.org/10.1017%2FS0266267113000096
• Crowd infallibility holds because the average covariance between voters becomes small as the population becomes large. https://doi.org/10.1016%2Fj.jmateco.2017.06.001

Diverse Capabilities

to be added...

[rmaniv]

prediction markets vs prediction polls - https://doi.org/10.1287/mnsc.2015.2374

experiment on committee votes - https://doi.org/10.3390/g10020020