Understanding Probability and Equality in Binary Choices

  • Context: Undergrad 
  • Thread starter Thread starter jk22
  • Start date Start date
  • Tags Tags
    Binary Choices
Click For Summary
SUMMARY

The probability of achieving an equal number of results from 2n binary choices is accurately represented by the formula C(2n,n)/2^(2n). For large values of n, such as n=1 million, this results in a significant probability of approximately 1/2000. This phenomenon raises concerns in voting scenarios, where a small number of votes can disproportionately influence outcomes, leading to interpretations of a "hidden dictator" effect in decision-making processes.

PREREQUISITES
  • Understanding of combinatorial mathematics, specifically binomial coefficients.
  • Familiarity with probability theory and its applications in binary outcomes.
  • Knowledge of voting systems and their statistical implications.
  • Basic grasp of statistical significance and its relevance in large sample sizes.
NEXT STEPS
  • Research the implications of binomial distributions in large-scale voting scenarios.
  • Explore advanced combinatorial techniques, particularly in relation to C(n,k) calculations.
  • Study the concept of statistical anomalies in voting outcomes and their interpretations.
  • Investigate the effects of voter turnout on election results and decision-making dynamics.
USEFUL FOR

Mathematicians, statisticians, political scientists, and anyone involved in analyzing voting systems and binary decision-making processes.

jk22
Messages
732
Reaction score
25
Suppose we have 2n binary choices. Then the probability of having the same number of results is :

C(2n,n)/2^(2n) ?

I don't know if this is true, since for the case n=1million, we have a probability as high as 1/2000, which seems quite important ?
 
Physics news on Phys.org
jk22 said:
Suppose we have 2n binary choices. Then the probability of having the same number of results is :

C(2n,n)/2^(2n) ?

I don't know if this is true, since for the case n=1million, we have a probability as high as 1/2000, which seems quite important ?

Your estimate seems about right. What is that a concern?
 
this was about votations : if we suppose 2 million 1 people vote a law then the highest probability is that only 1 voice makes the difference. I heard some people intepret this as there exist a sort of hidden dictator, but in fact we don't know who made the balance choice.
 

Similar threads

  • · Replies 18 ·
Replies
18
Views
4K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 19 ·
Replies
19
Views
4K
  • · Replies 13 ·
Replies
13
Views
3K
  • · Replies 29 ·
Replies
29
Views
6K
  • · Replies 131 ·
5
Replies
131
Views
10K
  • · Replies 16 ·
Replies
16
Views
2K