Re^4: Randomly choosing from a set of alternatives with varying popularity

> I'm curious to know how my other objection is handled. The order in a Perl hash is random, but fixed during a run. So this algorithm will be biased to some results.

OK, after a second coffee I finally got my had wrapped around it.

Definition/Interpretation matters:

The random pick $r between from 0..N-1 represents what the voter $r has chosen.

Hence order doesn't matter as long as it is fixed, since a 100 wide interval will always have the same probability of 100/550, no matter where it occurs.²

But I don't see any intuitive way to invert this interpretation, because $r has not-voted to all other choices.

Assigning "inverted" votes like suggested in your other post might work, as long as they sum up to 550 again°. But the question of the weighting factor and distribution will come up again.

Cheers Rolf
_{(addicted to the Perl Programming Language :)

Wikisyntax for the Monastery}

°) respectively N' is corrected.

update

²) IOW no matter if voters John and Jim swapped their place, their probability to be chosen stays the same.

Comment on Re^4: Randomly choosing from a set of alternatives with varying popularity Download Code

Replies are listed 'Best First'.
Re^5: Randomly choosing from a set of alternatives with varying popularity by ibm1620 (Hermit) on Mar 28, 2022 at 13:45 UTC
I'm curious why the order in which the hash is traversed would matter at all. I tried both sorting and shuffling the hash keys on each roll of the dice and the overall distribution of choices remained (approximately) the same. Seems to me that as long as the percentage of votes remains the same, the randomness of the dice ensures that over time it'll land on each animal that percent of the time. Example when 'popular' shuffles the candidate list each time. (Note that now the distribution of votes isn't linear.) `==> alligator:1000 bear: 900 cat: 800 dog: 700 elephant: 600 fox: 100 +giraffe: 10 hippo: 1 (Total votes: 4111) POP alligator: 977 bear: 933 cat: 804 dog: 720 elephant: 571 fox: 99 +giraffe: 6 hippo: 1 (Total votes: 4111)` [download] I also tried sorting the candidates in both ascending and descending order. Same result.	[reply] [d/l]
Re^6: Randomly choosing from a set of alternatives with varying popularity by LanX (Saint) on Mar 28, 2022 at 16:11 UTC
> I'm curious why the order in which the hash is traversed would matter at all. It doesn't for this special algorithm, like already explained here But if you want the inverse - however "inversion" is defined - you need to build a new hash with accordingly "inverted" weights, like demonstrated here. Cheers Rolf _{(addicted to the Perl Programming Language :) Wikisyntax for the Monastery}	[reply]