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While I myself don't queue dodge, I do understand the simple fact that some people have fun by winning and going into a game with the worst possible comp etc is just asking to achieve quite the opposite.
So I propose a simple system for dealing with it basically the queue system is suppose to find players of similar elo ratings & mash them together to hopefully form a team of similarly skilled people (although I question that, maybe champion based elo ratings would work out, another time for that idea I suppose).
My suggestion is that in addition to the above add another tally to check how many times you've dodged in a given period of time (say a 3 month rolling period) so players that are less picky are grouped together first while queue dodgers are essentially punished for being picky.
In theory it should work out for them more because if the people who are dodging it are doing it for the same reason (Team compositions, skills etc). Then if there available pool is shrunk it should be more likely to group them up with more like minded individuals.
This should allow the people who want to play do so, while allowing the players hoping to secure a victory do so at the penalty of taking longer to group etc.