# Opinions needed on changing states in a Markov Chain

Important Edit: Gave the wrong paper in the link

I am trying to implement the MC4 Markov Chain for a rank aggregation of search results. The equation states:

Select a random page $P$ from the set of all of the search results $S$. Select another random page $Q$ from $S$. If the rank of $Q$ is better (i.e. a lower number) than the rank of $P$ in the majority (=>50%) of the search engines that ranked both $P$ and $Q$, move to $Q$ and $M_p{_q}=1$, else stay at $P$ and $M_p{_q} = 0$

I have a list of 3 search engines. In many cases, only 2 of the 3 search engines rank the same result. This leaves me with a problem in that 1 of 2 the engines will almost certainly rank one result over the other. It doesn't seem correct to say that it is more probable to move from P to Q if it only ranks better 1 out of 2 times. What are your opinions on this?

For those interested, here is a link to the article:

DeConde et al Go to page 6 for the definition

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