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The variant you describe is listed on the site under the name Compromise Chess.
Don't know if this variant has been published here, or the name of the original developer. But here's a nice little change in the standard rules of the Mad Queen variant. Each player, at their turn, writes down two distinct legal moves that they could perform. The opposing player chooses one of these. If there are no optional moves, such as might occur during a check, the player may simply perform that one. Have played this form many times and it can lead to some interesting tactics. First, your opponent must recognize the potential of both offered moves and select the one they would deem 'second best'. And though a weaker move may appear such, they can often turn the game. Second, reducing your opponents options and forcing a truly weak move as their 'second best'. Try it, you'll like it.
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