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Lately I have been encountering a lot of people in ranked play who cannot, or refuse to, play another position than the one they had in mind when the entered the queue. With very little time to discuss these things arguments devolve and the person who doesn't get to play what s/he wants, rather than do the honorable thing and dodge, picks the absolute worse character for the match, and trolls. On the flip-side (and this is in mostly normal games) a summoner will lock in, regardless of who calls what in chat, and then walk away from their keyboard, pretty much dooming the game to failure. These two actions wastes everyone's time and effort, and even a little bit of Riots money.
Here is what I suggest. A few years ago, shortly before I quit playing World of Warcraft, they implemented a queuing system whereby you selected the roll you were queuing for. In LoL we could select for the five positions available, Top, Mid, Jungle, Support, ADC. If no one selects jungle and two people select top then we have no jungle. Each person would check the list in order of the position they wanted. They would each have to select all five in a 18.104.22.168.5. ranking. If you really wanted to be ADC then you put the 1 there, and then 5 in jungle if that was your worst position. Odds are everyone would get their first or second pick. Resolve disputed by who has the best stats (use whatever you like to determine that) and move on. When the matchmaking starts everyone all ready knows who's in what position, and their is no arguing about it.
You could even go one step farther and only allow people to pick champions based on their position, if you are selected for ADC you can't pick Alistair as your champ etc. I don't see this as a particularly hard thing to implement and should be pretty easy for everyone to get used to.