Well, the far more simple solution is to fix the bug that is causing Influence starbases to MULTIPLY, as opposed to ADD, like all other bonuses do.
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I also use the flipping to quicken military victory on the larger maps. But I agree that the culture bonuses should just add, not multiply. That would help considerably.
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The problem is NOT that influence needs to be capped. The problem is that multiple culture starbases in the same sector have their effect MULTIPLY, not add. They really should just add.
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Sorry fellas -- I don't wish to sound rude, but you're all wrong.

Okay, lets have the influence bonus add instead of multiply. That's fine by me. But I can still flip planet after planet with little or no resistance, it will just take a little longer, that's all. This will just add tedium to the game, not strategy. The best way to fix it is to have the A.I. counter agressivily with it's own starbases. Isn't that what a human opponent would do, short of engaging in open warfare?