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Captain should ban and then select support.
If someone is willing to trade for support that's nice of them, yet support should be selected first. This is because support is least likely to be countered by the other team.
If your team has First Pick:
1st pick should select support. This is to prevent being countered, and countering possible picks effectively pseudo-banning. For example Soraka counters Karthus before he can be picked.
2nd and 3rd pick should counter the other teams 1st and 2nd pick.
4th and 5th should counter the other teams 3rd and 4th.
If your team has Second Pick:
1st and 2nd pick should be jungler and counter their first pick(if support then counter with a solo bot pick)
3rd and 4th pick should counter the other teams 2nd and 3rd
5th pick should be a roamer or if the 2v1 bot is to strong then use 5th counter their bot combo.
***This is the beginning of an idea I have for a new matchmaking system.