In a Pairwise competition how to define a number of rounds which will give each option at least a few appearances
Currently an entry of 32 options with 64 rounds will leave a number of options with no appearances at all .
Is there a rough formula to use
The idea behind pairwise comparison is not that every individual participant sees or compares all options. Instead:
The cognitive load per participant is low, while the statistical reliability comes from aggregating many votes.
Because PollUnit pairs options randomly, there is no guarantee that every option will be shown. The probability of an option appearing can only be increased by increasing the number of rounds.
With N options and R rounds (each round is one comparison, showing two options):
avg = 2R / N
With 32 options and 64 rounds, each option appears 4 times on average.
Because pairing is random, appearances are uneven. To be very likely (99%) that an option appears at least once, you need roughly four times as many rounds as options.
May I ask what exactly your use case is? Do you want every participant to compare each option exactly once? If so, I could discuss this as a feature request in the team.
Many thanks for your reply . Our use case is probably not what the software is designed for but it is the best option for our planned competition that we currently have
Participating members have submitted 2 images each giving us 24 images in the comp .
All of our members attending will vote on each pair of images with show of hands . so there is in fact only 1 vote on each pair by everyone attending the meeting
We will be voting fast but I want to make sure that all members have a reasonable change of appearing at least twice in the selection process
We don't have time for 96 (4x24) rounds so I plan to split the entries into 2 groups of 12 each , with the top 4 in each group going into the playoff group
I planned to use 24 rounds for the groups of 12 and 16 for the final group of 8
That would give us 64 rounds which in timing terms would give us a workable session
According to your formula the average appearance in each group should also be 4 , with the proviso understanding that some images might be lucky and some unlucky
Thank you for sharing your use case with me!
I’ve been thinking about how we could improve our system to better support your requirements. While I haven't discussed this with our developers yet, I wanted to share an idea with you:
Would it be helpful if we implemented a feature that automatically generates rounds so that each voter sees every option exactly once? For this to work, the number of options would need to be even. If the number is odd, we would simply need to exclude one random option for each voter to maintain the balance.
If you have 32 options, each voter would complete 16 rounds. The pairs would still be picked randomly, but the system would ensure that each participant sees every option exactly once. What do you think?