To: Chair, Faculty Development Committee

From: Thomas Luckett

Date: 12 May 2010

RE: formally unresolvable travel grant rules

The deceptively simply rules governing travel grant requests read exactly as follows: "Requests of up to $1,500 per individual for travel funds may be made to the Faculty Development Committee. Per the current contract, the Faculty Development Committee shall not approve travel requests unless the request is matched by at least $100 in department [sic], grant, contract, or personal funds. Further, for requests over $750, a match of 20% of the total estimated travel cost is required."

Let C = "cost of the trip," R = "amount requested," and M = "matching funds," such that:

• C = M+R

The rules as stated show how to calculate the value of M for a known value of R, as follows:

• If: R < $750, then: M = $100
• If: $750 < R < $1500, then: M = 0.2*C
• If: R = $1500, then: 0.2*C < M = C-$1500

Faculty members applying for grants, however, do not begin with a known value of R and then calculate C and M. They begin with a known value of C (by adding up their airfare, lodging, registration, etc.), and then try to calculate R and M. If we express the above "if" statements as functions of C, then we get the following rules.

• If: $100 < C < $850, then: M = 100
• If: $937.50 < C < $1875, then: M = 0.2*C
• If: C > $1875, then: M = C-$1500

With the rules expressed in the above form, the problem becomes apparent. There is no rule when $850 < C < $937.50. Within this range, if you subtract 20% from C, then R is less than $750, and the 20%-rule does not apply. But if you subtract $100 from C, then R is greater than $750, and the $100-rule does not apply. There must therefore be another rule that has not been stated. Take a simple example:

The total estimated cost of my trip is $900. What is the amount of my request? If I request $750, and match $150, then this violates the rule that requests of $750 or less should be matched by $100. If I request $800 and match $100, then this violates the rule that requests of more than $750 should be matched by 20% or the cost. If I split the difference and match $125, then I violate both rules at once.

Someone might point out that the rule actually states that the request must be matched by "at least" $100, but these words "at least" do nothing to tell me how the amount of my matching funds should actually be calculated when it can be neither $100 nor 20% of cost. I suspect (though this is simply guesswork on my part) that the committee was thinking of the following unstated rule:

• If: $850 < C < $937.50, then: M = C-$750

If so, then the rule needs to be made explicit. I suggest a statement that would be something like the following:

"The Faculty Development Committee shall not approve travel requests unless the request is matched by departmental, grant, contract or personal funds in the following amount:

• For total estimated travel cost of $850 or less, matching funds of $100.
• For total estimated travel cost greater than $850 but not greater than $937.50, matching funds equal to the difference between the travel cost and $750.
• For total estimated travel cost greater than $937.50 but less than $1875, matching funds equal to 20% of the travel cost.
• For total estimated travel cost of $1875 or more, matching funds equal to the difference between the travel cost and $1500."

The problem with this version, however, is that it seems unnecessarily complex. Do we really need four categories? Perhaps we could eliminate the second category as follows:

"The Faculty Development Committee shall not approve travel requests unless the request is matched by departmental, grant, contract or personal funds in an amount equal to the greatest of the following:

• $100, or
• 20% of the total estimated travel cost, or
• the total estimated travel cost minus $1500."

In other words, we could reduce a lot of the complexity by eliminating the idea that $750 in requested funds is a cut-off point for the 20%-rule. Of course this would have the effect of raising the amount of the required matching funds to 20% of cost when $500 < C < $937.50, which may be considered a disadvantage.