With kids, some problems are a good fit for randomization. Perhaps you're doing a bath and both kids want to be the second one to have their hair washed, so you propose flipping a coin. The kids understand that they can't both be second, and flipping for it seems fair.

Or, at least, it seems fair right up until you flip the coin and one of them loses. Then there are suddenly all sorts of overlooked issues and last-minute considerations ("I had to go first last time!", "I have longer hair!").

The way I deal with this is by confirming buy-in before randomization. I won't randomize unless they agree that we should resolve this randomly, that they will abide by the results without fussing, and that if they do fuss it's time-out. Even though they know this rule with me, I still repeat it every time: it doesn't take that long compared to the rest of the process, and it being fresh in their minds when we randomize works much better.

In cases where the randomization is for their benefit ("which park should we go to?", "who gets the first Nora cuddle?"), if they don't accept the terms we can fall back to neither. In other cases, though, where I need to impose randomization, I'll be mildly coercive: if one of them won't agree to these terms I say I'll resolve it in the other's favor. At which point they prefer half a chance of getting their way to no chance, decide to participate, and confirm they won't fuss.

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[ epistemic status: one size does not fit all - this is mental exploration, not advice nor disagreement with a system that works for you. ]

I know of many kids who take turns or let the oldest choose, or have a schedule, rather than randomizing.  The common denominator among them and your story seems to be the "fallback to neither" and "time-out for whinging" elements, not the decision mechanism nor the prior explicit buy-in.

Be aware that this inherently penalizes children who dislike uncertainty.

Take two cases:

  1. You have a schedule for who does chore X, balanced 50/50.
  2. You flip a coin for who does chore X, every time.

For someone who doesn't mind uncertainty, these are effectively equivalent. For someone who does mind uncertainty, 2 is worse than 1, often far worse.

I see, by "this" you meant using randomization in general, but getting buy-in?

I agree. And, in general, I don't think it makes sense to use randomization when there are other good options. If both kids agreed to do (2) I'd help them with it and enforce the outcome, but otherwise it would be (1).

I see, by "this" you meant using randomization in general, but getting buy-in?

Yes.

If both kids agreed to do (2) I'd help them with it and enforce the outcome, but otherwise it would be (1).

...which in the case of two kids, of of which minds uncertainty more than the other, penalizes the child who dislikes uncertainty. "Do X or I won't allow a schedule"[1] becomes a valid threat.

  1. ^

    Or rather, subtler versions thereof.

which in the case of two kids, of of which minds uncertainty more than the other, penalizes the child who dislikes uncertainty. "Do X or I won't allow a schedule" becomes a valid threat.

Sorry, that's not what I'm saying. For something that is a good fit for a schedule, like a chore rotation, a schedule would be the default. Only if both kids wanted randomization would we do that. Which means that if one kid didn't like randomization, we wouldn't.

Ah, I thought you meant "if both kids agreed to a schedule you would, otherwise it would be randomization". Looking back, I missed that you meant the other way around.

They'll get the dispreferred outcome more frequently since their sibling will agree.