# Representative Government and Environmental Management

By Edwin T. Haefele | Go to book overview

Table B.3. Probability of Trading (3 × 5 voting matrix)
Case Strong
ordering
set
Rotation
set
Strong
indifference
set
Random
set
300 zero zero zero zero
211 (2)a .39 .33 .19 .11
203 (3) .54 .48 .28 .17
130 (3) .54 .48 .28 .17
122 (4) .70 .63 .43 .27
122A (4) .75 .68 .49 .31
041 (5) .81 .75 .54 .36
Note: All calculated on equal likelihood basis and rounded to 2 decimal places.
aNumbers in parentheses indicate number of traders.
 Case 300 Case 211 Case 203 Y Y Y N N Y Y Y N N Y Y Y N N Y Y Y N N Y Y Y N N Y Y N Y N Y Y Y N N Y Y N Y N Y Y N N Y Case 130 Case 122 Case 122A Y Y Y N N Y Y Y N N Y Y Y N N Y Y N Y N Y Y N N Y Y Y Y N N Y N Y Y N Y N Y Y N Y N N Y Y Case 041 Y Y Y N N Y Y N Y N N N Y Y Y

Although the overall level of probabilities is an artifact of the preference set chosen, some additional evidence of variation as issues are added is given in figure B.3, which uses the rotation set. It should be noted that, no matter what preference set is chosen, the probability of trading can only approach unity. There is always one non-trading vector set--when all preference orderings are identical.

CONCLUSIONS

In "real" situations, each legislator will have, of course, only one preference vector instead of several, and the probability of trading in any legislature, commission, or committee will be a function of that one vector set. It may be worthwhile, however, when devising new commissions, special districts, or other decision structures, to take some note of the number of independent issues likely to come before such bodies and to examine the

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