K. J. Arrow “Social Choice: Personality and Multi Criteria”, example p. 42

The candidate set of environment A (S_A): x, y, z, w

The candidate set of environment B (S_B): x, z, w

Note: Environment B removed candidate y

Generalization K. J. Arrow’s example

The candidate set of environment A (S_A): Y₁, Y₂,・・・, Y_i,・・・, Y_k

The candidate set of environment B (S_B): Y₁, Y₂,・・・, Y_i, Y_r,・・・, Y_s

Note: Environment B, removed candidates Y_i+1・・・ Y_k ; added candidates Y_r,・・・, Y_s