<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>

CC BY-SA 4.0
2020-03-09T01:09:19.603Z
2020-03-09T01:09:19.603Z
Mr-Programs
<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>

CC BY-SA 4.0
2020-12-04T11:19:58.083Z
Where did you get this text/screenshot from? Which book, article, etc.?
nbro
CC BY-SA 4.0
2022-12-25T04:01:19.087Z
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.
Snehal Patel
<probability><ensemble-learning>
Why does the error ensemble use the ceiling of the number of classifiers?
Mr-Programs
# 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.  

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## 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


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