So let's assume information is classified as Amount of PRs, Type of PRs, and Who the PRs are.
Without claiming,
Mafia knows
1. Amount of Mafia PRs
2. Type of Mafia PRs
3. Who the Mafia PRs are
4. Amount of Town PRs
Town knows nothing.
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With claiming,
Mafia knows
1. Amount of Mafia PRs
2. Type of Mafia PRs
3. Who the Mafia PRs are
4. Amount of Town PRs
5. Who the Town PRs are
Town knows
1. Amount of Mafia PRs
2. Amount of Town PRs
3. Who the Town PRs are
___________________________________________________________________________
Well, Town gets 3x the information compared to Mafia and the thing they don't know (exact mafia PRs) doesn't affect them too much, so yeah, I think that's a good tradeoff, personally.