Answers.Body: <blockquote>
    <p>Y ensemble size voting wrong</p>
    
    <p>k = 50% or majority threshold</p>
  </blockquote>
  
  <p>If you have 11 models. Then the majority of models is anything bigger than 50% of the number of ensemble models. In the example where you have 11 base models. The majority would be anything bigger than N/2 or 11/2. But since 11 is an odd number and cannot be divided by 2. We have to use the python ceiling function to round 5.5 to 6. The in other words. For your ensemble to be wrong. We must look for the probability that Y of them are wrong. Y is ≥ than K and K is ceil(N/2). Thus we must calculate this probability(6 wrong) like shown above summating the possibility of each of these discrete combinations into one</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-03-09T01:09:19.603Z
Answers.LastActivityDate: 2020-03-09T01:09:19.603Z
Answers.UserDisplayName: Mr-Programs
Body: <p><a href="https://i.sstatic.net/Wybwm.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Wybwm.jpg" alt="error ensemble" /></a></p>
  <p>What is <span class="math-container">$y$</span>? Why is <span class="math-container">$k$</span> the ceil of <span class="math-container">$n/2$</span>? What is <span class="math-container">$y \geq k$</span>?</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-12-04T11:19:58.083Z
Comments.Text: Where did you get this text/screenshot from? Which book, article, etc.?
Comments.UserDisplayName: nbro
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-12-25T04:01:19.087Z
Comments.Text: This [SE:AI post](https://ai.stackexchange.com/questions/38051/how-can-an-ensemble-be-more-accurate-than-the-best-base-classifier-in-that-ensem) will shed light into the application of the binomial probability to this problem of ensembles.
Comments.UserDisplayName: Snehal Patel
Tags: <probability><ensemble-learning>
Title: Why does the error ensemble use the ceiling of the number of classifiers?
UserDisplayName: Mr-Programs
ThreadText: # Why does the error ensemble use the ceiling of the number of classifiers?
  
  (Asked by: username_0 on 2020-03-08)
  
  [![error ensemble](https://i.sstatic.net/Wybwm.jpg)](https://i.sstatic.net/Wybwm.jpg)
  
  What is $y$? Why is $k$ the ceil of $n/2$? What is $y \geq k$?
  
  **Tags:** probability, ensemble-learning
  > **Comments:**
  > **username_1**: Where did you get this text/screenshot from? Which book, article, etc.?  
  > **username_2**: This [SE:AI post](https://ai.stackexchange.com/questions/38051/how-can-an-ensemble-be-more-accurate-than-the-best-base-classifier-in-that-ensem) will shed light into the application of the binomial probability to this problem of ensembles.  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_0 on 2020-03-09. Score: 1
  
  > Y ensemble size voting wrong
  >
  > k = 50% or majority threshold
  
  If you have 11 models. Then the majority of models is anything bigger than 50% of the number of ensemble models. In the example where you have 11 base models. The majority would be anything bigger than N/2 or 11/2. But since 11 is an odd number and cannot be divided by 2. We have to use the python ceiling function to round 5.5 to 6. The in other words. For your ensemble to be wrong. We must look for the probability that Y of them are wrong. Y is ≥ than K and K is ceil(N/2). Thus we must calculate this probability(6 wrong) like shown above summating the possibility of each of these discrete combinations into one
  
  
  ---
  
  