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Wouldn't it make sense that the electrode with the higher reduction potential be the cathode, since reduction occurs at the cathode?

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No you misunderstand the meaning of reduction potential. Reduction potential refers to the voltage required to reduce a material under standard conditions. If a material has a higher reduction potential it takes more energy to reduce it than a lower reduction potential material. Therefore the higher reduction potential material is actually oxidized to reduce the lower reduction potential material.

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