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POHow should I order these "helpful" scores?
 

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    <p>Under the user generated posts on my site, I have an Amazon-like rating system:</p> <pre><code> Was this review helpful to you: Yes | No </code></pre> <p>If there are votes, I display the results above that line like so:</p> <pre><code> 5 of 8 people found this reply helpful. </code></pre> <p>I would like to sort the posts based upon these rankings. If you were ranking from most helpful to least helpful, how would you order the following posts?</p> <pre><code> a) 1/1 = 100% helpful b) 2/2 = 100% helpful c) 999/1000 = 99.9% helpful b) 3/4 = 75% helpful e) 299/400 = 74.8% helpful </code></pre> <p>Clearly, its not right to sort just on the percent helpful, somehow the total votes should be factored in. Is there a standard way of doing this?</p> <p><strong>UPDATE:</strong></p> <p>Using Charles' formulas to calculate the Agresti-Coull lower range and sorting on it, this is how the above examples would sort:</p> <pre><code> 1) 999/1000 (99.9%) = 95% likely to fall in 'helpfulness' range of 99.2% to 100% 2) 299/400 (74.8%) = 95% likely to fall in 'helpfulness' range of 69.6% to 79.3% 3) 3/4 (75%) = 95% likely to fall in 'helpfulness' range of 24.7% to 97.5% 4) 2/2 (100%) = 95% likely to fall in 'helpfulness' range of 23.7% to 100% 5) 1/1 (100%) = 95% likely to fall in 'helpfulness' range of 13.3% to 100% </code></pre> <p>Intuitively, this feels right.</p> <p><strong>UPDATE 2</strong>:</p> <p>From an application point of view, I don't want to be running these calculations every time I pull up a list of posts. I'm thinking I'll either update and store the Agresti-Coull lower bound either on a regular, cron-driven schedule (updating only those posts which have received a vote since the last run) or update it whenever a new vote is received.</p>
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