1.2.2.1 Elected Faculty Membership The 94 elected faculty seats shall be apportioned each spring among the colleges and the University Libraries according to the following two equally weighted factors based on data for the preceding fall semester: (1) the number of the following individuals, all of whom shall be considered "faculty" for purposes of this Rule: (a) full-time faculty with the rank of assistant professor or higher, (b) full-time faculty appointed in the clinical, extension, librarian, research, and specialclinical title series, and (c) full-time lecturers and instructors; and (2) the number of full time students enrolled in the college, computed so that students enrolled in the Graduate School shall be assigned to the college in which they are pursuing their studies. (US: 10/12/81 and BofT: 4/6/82; BofT: 12/11/84; US: 10/11/99 BoT 1/22/02:) The apportionment of the seats is based on a “population fraction”, Pu, calculated as:Ideally, the fraction of the total faculty Senate seats which would be apportioned to an academic unit would be obtained by using the following formula:

Pu = 1/2 (Fu/Fe + Su/Se)

where Fu and Su are respectively the number of eligible faculty and the number of full-time students in the unit, and Fe and Se are the total eligible faculty and students, respectively, in all units.

The apportionment of the seats is calculated using the method of equal proportion used by the Census Bureau in calculating Congressional seats. A formula is used to calculate “priority values” for the nth seat (i.e. 1st, 2nd, 3rd, 4th, etc.) for each college according to:

Priority value for the nth seat of each college = Pu/[n(n-1)]1/2

The seats are assigned based on the above priority values until all seats are allocated. In case of a tie in granting the last seat, the college with smaller number of allocated seats up to that point is awarded the seat. Any further tie is resolved by a random draw. (For an example of this calculation method, see Appendix A.)

Example: we have 10 seats to be allocated to the following three colleges:

College A with the population index of 0.2

College B with the population index of 0.3

College C with the population index of 0.5

College / Iu = Index / n / Priority value =
A / 0.2 / 1 / Large
A / 0.2 / 2 / 0.141421
A / 0.2 / 3 / 0.081650
A / 0.2 / 4 / 0.057735
A / 0.2 / 5 / 0.044721
B / 0.3 / 1 / Large
B / 0.3 / 2 / 0.212132
B / 0.3 / 3 / 0.122474
B / 0.3 / 4 / 0.086603
B / 0.3 / 5 / 0.067082
B / 0.3 / 6 / 0.054772
C / 0.5 / 1 / Large
C / 0.5 / 2 / 0.353553
C / 0.5 / 3 / 0.204124
C / 0.5 / 4 / 0.144338
C / 0.5 / 5 / 0.111803
C / 0.5 / 6 / 0.091287
C / 0.5 / 7 / 0.077152
C / 0.5 / 8 / 0.066815

Shown below are the same data as above sorted according to the priority values. In addition the awarded seats are determined and shown:

College / Iu = Index / n / Priority value = / awarded
seat #
A / 0.2 / 1 / Large / 1
B / 0.3 / 1 / Large / 2
C / 0.5 / 1 / Large / 3
C / 0.5 / 2 / 0.353553 / 4
B / 0.3 / 2 / 0.212132 / 5
C / 0.5 / 3 / 0.204124 / 6
C / 0.5 / 4 / 0.144338 / 7
A / 0.2 / 2 / 0.141421 / 8
B / 0.3 / 3 / 0.122474 / 9
C / 0.5 / 5 / 0.111803 / 10
C / 0.5 / 6 / 0.091287
B / 0.3 / 4 / 0.086603
A / 0.2 / 3 / 0.081650
C / 0.5 / 7 / 0.077152
B / 0.3 / 5 / 0.067082
C / 0.5 / 8 / 0.066815
A / 0.2 / 4 / 0.057735
B / 0.3 / 6 / 0.054772
A / 0.2 / 5 / 0.044721

College A = 2 seats

College B = 3 seats

College C = 5 seats

Usually the portion of the total faculty seats which would be ideally assigned to a unit will not be a whole number. For each unit a certain inequity will result, this being the non-negative deviation of a unit's actual percentage from its ideal percentage of the seats. The seats shall be apportioned to the units in a manner which minimizes the total inequity, subject to the condition that each unit gets at least one seat . If two units have identical ideal percentages and the minimum would be attained by giving them different representations, then the extra seat shall be allocated to one of them by a random process.) An administrative title below that of Dean shall not automatically make the holder ineligible.