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Discussing "events" (ie, Truth Booth or Match Up) together muddles the analysis a bit.
I agree with Medea above that a Truth Booth should give at most 1 bit of information.
Would've been a great Pudding post imo, but oh well, happy to find this nice devblog instead.
It’s mostly about how to elicit the information from the contestants. Once you have the probabilities from them, it seems relatively straightforward.
Earlier quoted context omitted.
Because when it's true, you also learn about any prior match ups involving those two people.
That's not how information works. Learning more from one outcome than the other decreases the probability of that outcome occurring, so the expected information (which is the sum of the outcome probability times the outcome information for each of the two possible outcomes) is always less than or equal to one. If all you can get is a "true" or "false" you expect, at most, one bit of information.
Earlier quoted context omitted.
Because when it's true, you also learn about any prior match ups involving those two people.
That's not how information works. Learning more from one outcome than the other decreases the probability of that outcome occurring, so the expected information (which is the sum of the outcome probability times the outcome information for each of the two possible outcomes) is always less than or equal to one. If all you can get is a "true" or "false" you expect, at most, one bit of information.
A true answer for a potential match is actually a state update for all of the (n-1) edges connecting either contestant, that's 2(n-2) edges that can be updated to be false. Some of these may already be known from previous rounds' matchups but that's still more than a single binary.
They have an example that calculates the expected information gained by truth booths and all of the top ones are giving more than one bit. How can this be? It is a yes/no question a max of 1 bit should be possible
Because when it's true, you also learn about any prior match ups involving those two people.
Fun post. I'd be interested to know: How many consecutive Truth Booths (or: how many consecutive Match Ups) are needed to narrow down the 10! possibilities to a single one? Discussing "events" (ie, Truth Booth or Match Up) together muddles the analysis a bit. I agree with Medea above that a Truth Booth should give at most 1 bit of information.
I saw an episode of this and felt the contestants didn’t seem that interested in winning the money. Just romance. I was curious how suboptimally they tended to play.
For a start, the setting is an emotive one. It's not just a numeric game with arbitrary tokens, it's about "the perfect romantic partner." It would take an unusually self-isolating human to not identify who they feel their perfect match should be and bias towards that, subconsciously or consciously. We (nearly) all seek connection.
Then, it's reality TV. Contestants will be chosen for emotional volatility, and relentlessly manipulated to generate drama. No-one is going to watch a full season of a handful of math nerds take a few minutes to progress a worksheet towards a solution each week coupled with whatever they do to pass the time otherwise.