Argument: in ARAM, if you are considering dodging, you almost certainly should, because no one on the other team has.
Assumptions: You can pick the winner of roughly 80% of ARAM games just by looking at team composition. Most people prefer being on the winning side of that than the losing side. The penalty for dodging is less than the penalty for playing a hopeless game, in the sense that you can waste 20 minutes in a game you cannot possibly win or spend a similar amount of time doing something else while waiting out your dodge penalty. And here is the critical assumption: you can tell if your team composition is bad, and you are likely to dodge if (before seeing the other team) you think your team is likely to be worse than the opposing team.
If you think your team composition is better than average, you are very unlikely to dodge. If you think your team is about average or slightly worse, you are not very likely to dodge. If your team is bad, you are somewhat likely to dodge. And if your team composition is horrible, you are very likely to dodge. But you already knew that, so what am I trying to add here?
The decision is symmetrical, with the other team facing the same decision. Given that no one on the other team has not dodged, you must find it very unlikely that their team composition is horrible and somewhat unlikely that their team composition is bad. (And remember, each of 5 people can dodge, so none of the 5 said “not worth it” and dodged.) Now re-assess your chances given that. If your team composition is bad, it is not only that your team is below average, but also that the opposing team has not signaled (by dodging) that their team is bad or worse. Five people on the opposing team think they have a good enough chance of winning with their team composition. Given that, how confident are you of your team composition?
Applying this recursively would leave us only playing with “above average” teams, because someone would dodge unless the team composition on both sides was at least “good.” (If all the horribly composed teams dodge, that means “bad” is as bad as it gets, so all the badly composed teams dodge, which means “average” is as bad as it gets…) But what is one to expect from a game mode where randomness dominates? But then, why are you playing ARAM if you are not comfortable with the “AR”?