PART 01
候选集合Candidate set
猫、狗、鸟是这次互斥的所有候选结果。Cat, dog, and bird are all mutually exclusive outcomes here.
01 · 只有一整杯01 · Only one whole cup
如果“猫”的可能性多拿一点，另外两个候选能不能都保持原样？If “cat” receives more probability, can both other candidates stay unchanged?
02三杯概率水Three Cups of Probability Water
守恒重分配型Conserved reallocation三杯总量Total volume
1.000
始终守恒always conserved
最大候选Largest candidate
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当前最高杯highest cup now
最近操作Last changed
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获得指定份额received requested share
检验方法：记住两只杯子的高度，再把第三杯调高。至少一杯必须下降，总量仍显示 1.000。Verification: note two cup levels, then raise the third. At least one other cup must fall while the total still reads 1.000.
03一份分布的 3 个条件Three Conditions of a Distribution
候选 + 份额Candidates + sharesPART 02
非负份额Non-negative shares
每只杯子的水位只能在 0 与 1 之间。Every cup level stays between zero and one.
PART 03
总量为 1Total equals one
三杯共同瓜分完整的可能性总量。The three cups divide the whole amount of possibility.
CHECK
此消彼长Trade-off
一杯上升时，其他杯必须让出同样总量。When one rises, the others must give up the same total.
04最小机制：所有候选共同分 1Minimal Mechanism: All Candidates Share One
Σ pi = 1pcat + pdog + pbird = 1
上方每次滑动后都重算另外两杯，使 pi ≥ 0 且总和精确回到 1。Every slider move recalculates the other two cups so each pi stays non-negative and the total
returns exactly to one.
提高一杯Raise one cup指定新的概率份额Set a new share
挤压其余杯Compress the others按原比例让出水量Give up water proportionally
总量守恒Conserve total重新相加仍为 1The sum remains one
05边界实验：检验一组伪概率Boundary Test: Inspect a Fake Distribution
主动制造失败Create a failure声称 0.7 + 0.6 + 0.4Claim 0.7 + 0.6 + 0.4
三项都在 0 到 1 之间还不够；如果总和不是 1，它就不是完整概率分布。主实验的三杯不会被破坏。Keeping each item between zero and one is not enough. If the sum is not one, it is not a complete distribution. The three main cups remain conserved.
尚未执行。检查非负，也要检查总和。Not run yet. Check non-negativity and the total.
✗ 每项小于 1 就是概率分布。Values below one automatically form a distribution.
→ ✓ 还必须非负且全部加总为 1。They must also be non-negative and sum to one.
✗ 提高一个候选不会影响其他候选。Raising one candidate leaves all others unchanged.
→ ✓ 总量固定，提高一项必挤压其余项。With a fixed total, raising one must compress others.
✗ 最高概率就是必然发生。The largest probability is certain to occur.
→ ✓ 最高只表示在当前候选中占比最大。Largest means only the biggest share among candidates.
06 · 一句话带走06 · One line to keep