Assuming no interdependencies, equal costs, and that both beliefs matter in the longer time frame, I resolve the one with the higher risk first, measuring risk as the likelihood of being wrong times the cost of being wrong.
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Some risks, though very unlikely, have such catastrophic consequence that you want deal with it. For example, wearing helmets when riding horses.
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Minimax regret.
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pick the one which either is very monetizable or unlocks/derisks something very fun.
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Construct a payoff matrix.
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Prioritise the one you secretly want to deprioritise
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I’m much more basic and rudimentary I guess if there are no obvious interdependencies than I would flip a coin to decide priority
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Establish the consequences of each belief and then test the one which has the most -ve impact on me/people/my environment. e.g. If I a) believed the earth was flat and b) climate change was a hoax, I'd test b
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Taking beliefs not as isolated propositions but as parts of a web (fuzzy nodes). Then want to test first the one with the biggest effect on the global topology of the web.
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Maximize your capability to explore any new ideas you may get while waiting for the year to pass (Optionality on unknown unknowns.) If one experiment might be much more quick/cheap, do it first. Then you have the rest of the year to explore or have fun.
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