Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

Could you help me with the following questions? Exercise 7: Condorcet's Jury Theorem A person has allegedly committed a crime and a trial will take

Could you help me with the following questions?

image text in transcribed
Exercise 7: Condorcet's Jury Theorem A person has allegedly committed a crime and a trial will take place for a jury of 3 to declare him either innocent or guilty. Previous to the trial start, none of the jury members has any knowledge of the situation and being impartial jurors, if they had to convict now, they would decide with the following probabilities: P; (G | guilty) = P; (1 | innocent) = 0.5 where j refers to the jury number, G is a guilty vote (I is an innocent vote), and both probabilities are conditional probabilities over the underlying truth. (a) What's the probability the jury would make the correct choice if they had to de- cide at this moment? After the trial, the jurors have heard the evidence related to the crime and update their 3 probabilities to: P; (G | guilty) = P; (I | innocent) = 0.7 (b) Given this new state, what's the probability for the jury to make the correct decision if they had to decide at this moment? (c) What would happen if we were to consider 4 jurors instead of just 37 (assume, in the case of a tie, that the correct decision is made). (d) If the opportunity cost of each jury member is $150 and the benefit of making the right decision (compared to making the wrong decision) is $1000, would it make sense to increase the jury size from 3 to 4? what about decreasing the pool from 3 to 1

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Econometric Analysis

Authors: William H. Greene

5th Edition

130661899, 978-0130661890

More Books

Students also viewed these Economics questions

Question

Explain the strength of acid and alkali solutions with examples

Answered: 1 week ago

Question

Introduce and define metals and nonmetals and explain with examples

Answered: 1 week ago

Question

Praises, recognizes and values everyones contributions and effort.

Answered: 1 week ago