Studies and practices in China unanimously ignored the additivity of government performance evaluation index. In the present evaluation systems, the total score of government performance is added by simply putting the indexes values (numbers) together. Neither the researchers nor the practitioners pay any attention to the reality that the government performance evaluation indexes belong to high attribute dimensions, and they cannot be added directly. To process these high attribute indexes of government performance evaluation, we have to follow their clustering features and reduce dimensions to convert high attribute dimensions to low attribute dimensions. In this study, binary state variable was adopted to reduce dimensions. We reduce the dimension of the performance evaluation index by 4 steps: (1) separating the hazy description of into measurable sub-indexes; (2) treating each sub-index as a binary variable by judging it false or true; true and false are respectively indicated as 1 and 0 in the statistical software or mathematical language; (3) using the methods of aggregate degree, aggregate vector, and set theory to make the sub-indexes aggregate in a same class; (4) nondimensionalising the values of sub-indexes and realizing the additivity of all the sub-indexes.