# Simulate a process of state change with transition probability dependent on proportion in state in previous time

I was thinking about a reverse single transferable vote type situation (i.e. most votes is eliminated) where the process continues until there is only on state left and at each new round there really is a new vote. My suspicion is that this could be modelled by assuming like:

50% to most similar (remaining) state, 25% to next most similar state, 25% to next most similar state if present state is the most populous state

or

90% current state; 10% most similar state

This means that for each time period the number of states is reduced by one and presumes people opt for options most similar to their preference in the previous time period. That latter character reminds me in particular of Markov chains.

I would like to know how to think about doing this or what search terms would help to find someone else who has already tried this.

My instinct that it would be a bit like if you had for t=1, n=20 bins that marbles had fallen into and then count the number of marbles in each bin. For t=2, there are still n=20 bins but the most populated bin from the previous example has a 0% destination probability for all other bins/states and the destination probabilities for the other bins depend on their relationships to each other and, in particular, the "losing" bin. And the for t=3 there are now two bins with destination probabilities of 0% and so on... Being able to look at the situation for each t would be important, too.

Any language would be greatly helpful in a conceptual sense, but on a personal level I have even a cursory understanding of just R (but also some experience with and access to SAS and a bit less again, on both counts, with Stata).

Thank you (and apologies if this is in the wrong place).

• I think the process of having a preference list from each voter and then slowly eliminating the candidate with the least votes and checking the preference list again is exactly that and simulating it by markov chains might result in a different outcome. – Adder Jun 9 '17 at 11:49