# How to model the distribution of a word game in order to find correlation between demographics and chosen words

I have an experiment (in the form of a word game) whereby people are asked to choose a set of words to describe associations with a topic with the aim of having another person guess the topic. I record the order in which the clue words are chosen and the participant can choose as many words as they like from a given set (within some time limit) until the other person guesses correctly.

For example, participants might be given a set of words like {luxury, fast, convenient, expensive, affordable, necessary, mechanical, fun, ford, toyota, etc... } to describe the item "car." For any particular item there is 60 or so words to choose from with no limit on the number of words that may be chosen (within the time limit of the experiment).

Given that we know the demographics (male or female) of a large number of people that played the same game i.e., how they describe cars, what would be the best way to model this?

The aim is to determine the probability that a person is male or female after they play the same game (provided there was difference in the words that males and females chose).

I understand how this could be done if the order in which people chose certain words was irrelevant, and the number of words that were chosen was constant. In that case I could simply determine a correlation between individual words and gender. I am unsure how to approach this given that the order in which words are chosen seems important (the first word is most relevant and as people run out of words they become less relevant). Also the number of words chosen would be different per game.

I'm looking for some insight into how to approach this problem as it isn't clear to me how to go about this. I'm unsure if it fits a markov model (trail of thought while giving clues), multinomial hypergeometric distribution (as clue words arent replaced in the game) or if this can be as simple as applying weights depending on when a clue word given in the game. Any guidance would be greatly appreciated.