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Kernel Density Estimations: Condorcet's Jury Theorem, Part 5

number of experiments

observations

probability bias

0.03

population of voters

repeated extractions

repetitions

graph

density

cumulative density

random seed

theoretical probability of the right decisions by voting: 0.6896

observed mean probability of the right decision by voting: 0.65

standard error of the probability: 0.2934

Kolmogorov-Smirnov test statistic: 0.8087

Lilliefors test (reps. = 10)

significance	critical value
20%	0.217
15%	0.227
10%	0.2398
5%	0.2621
1%	0.3031

This is the fifth of five Demonstrations about Condorcet's jury theorem (1785). Here we show estimates of kernel density and cumulative kernel density functions for a given probability bias

and number of voters

—compare with Parts 3 and 4 in this series of Demonstrations (see Related Links). We test the goodness of fit of the observed right decision probabilities to normality. For reference, the test statistic table for the Lilliefors normality test is presented (the test statistic and null hypothesis are the same as the Kormogorov–Smirnov test for normality). The critical values presented are based on Abdi and Molin [1]; see their summary for the details of the test. Note also the Gaussian kernel is used in the kernel estimation.

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