Socio-Econ. Plan. Sci. Vol. 17, No. 2, pp. 83-86, 1983
0038--0121/83/020083--04503.00/0 Pergamon Press Ltd.
Printed in Great Britain.
A FINANCIAL PLANNING MODEL FOR PRESIDENTIAL CANDIDATES PATRICK G. McKEOWN and ANDREW F. SEILA College of Business Administration,University of Georgia,Athens, GA 30602, U.S.A.
(Received 7 September 1982) Abstract--The necessity of entering a sequence of interrelated state primarieshas forced presidentialcandidates to be much more deliberate in planning campaign finances. This paper presents a linear programming model for optimal allocation of time and money to each primary in order to maximize the number of delegates won. The model attempts to quantify and exploit the relationshipsbetween performance in early primaries and performance in later primaries, which has heretofore been labeled the "snowball effect." Finally, the model, whose major use would be in overall strategic planning,is illustrated with an example.
Bush devoted a great deal of time and money to the New Hampshire primary in March. His unexpected defeat depleted his campaign funds to such an extent that he could not mount an effective campaign in the California primary in June. Similarly, Edward Kennedy's early losses contributed to the failure of his fund-raising efforts which in turn led to a severe cutback in his campaign staff and reduced chances to secure primary victories . In this paper we propose a mathematical model of the resource allocation decisions facing the presidential candidate. This is a linear programming model whose objective function represents the total number of delegates won in the entire sequence of primaries/caucuses. Constraints in the model represent the relationships between a candidates performance in the primaries, future contributions, spending limits, and future vote-getting potential. In Section 2, we present the decision model. Section 3 contains a worked-out example, and in Section 4 we discuss the ramifications of the model.
In the years since 1968, the percentage of delegates to the two major political party conventions that are selected in state primaries and caucuses has increased from 40% to more than 70%. This increased emphasis on the primary process has drastically changed the decisions facing presidential candidates. At one time, a candidate could win his party's nomination without entering any primaries; now, a good showing in the primaries and caucuses is a virtual prerequisite to the nomination. At the same time that the major political parties were making rule changes that forced their candidates into the state primaries and caucuses, Congress was passing new laws that restrict contributions and spending in political campaigns, and that make federal campaign funds available to qualified candidates. The key provisions of these laws restrict contributions by individuals to no more than $25,000 per candidate in an individual year and contributions by a candidate to his/her own campaign to $50,00012]. Additional provisions restrict the amount that a candidate can spend on primaries in order to receive federal matching funds. Laws were also enacted by individual states which restrict primary campaign expenditures. The spending limits range from $3.9 million in California to $294,000 in New Hampshire . The combined effect of these new laws is to place the presidential candidate in a decision-making environment in which he/she must allocate available resources (time and money) in such a way as to maximize the delegates won in the primaries/caucuses. What the candidate, in fact, sees is a sequence of primaries/caucuses that are quite interrelated. A good showing in the first primaries has the effect of increasing the candidate's credibility and visibility, which, in turn, generates additional contributions and votes in succeeding primaries . This "snowball effect" could encourage the candidate to allocate much of their resources to the early primaries. On the other hand, if the resources allocated to early campaigns do not pay off in wins or near-wins, then resources available for later campaigns are diminished and so are the chances of winning. This consideration, therefore, would encourage the candidate to conserve funds for later primaries, in the hope that later wins can send the candidate to the party convention with sufficient momentum to win the party's nomination. Examples of these effects can be seen in the 1980 campaign. George
2. PROBLEM DESCRIPTION AND FORMULATION
We will use the term delegate selection process (DSP) to denote either a primary or a state caucus in the presidential campaign. The candidate (or his/her advisors) must decide how much time and money resources to allocate to each DSP in order to maximize the total number of delegates committed to the candidate prior to his/her party's national nominating convention. The candidate's strategy must represent his/her and his/her advisors opinions concerning: --the ability to win delegates in each DSP as a function of prior wins and time and money allocation to the DSP; --the ability to raise campaign funds as a function of previous performance; --the effectiveness of early versus later wins; --the desire for flexibility in allocation of time and money; and possibly other factors. The model we propose is a deterministic model. We recognize that the primary/caucus environment is stochastic; however, a stochastic optimization model would present possibly insurmountable problems in finding a solution. In addition, there is some reason to believe that campaign advisors would find the deterministic model 83
PATRICKG. McKEow~and ANDREWF. SEILA
easier to deal with conceptually. Uncertainties in the model can be explored using appropriate sensitivity analysis.
be converted into a linear programming formulation. To do this, we will let
Wj(p3 = w*pj, (8) Formulation Pj = p~. + pj,(Dj - D>t) + Pi285+ Pj3rj, (9) Suppose that there are n DSP's in the campaign. We will number them starting with the first DSP and pro- and ceeding to the last, so that DSP~ is the jth delegate G(pj, D3 = q* + cj,pj + c,2Dj. (10) selection process in the campaign. Now let: di be the level of campaign funds prior to making the allocation to In these linearizations of the functions, w *j is the total DSP~; t~ be the days from the beginning of the campaign number of delegates available to be won in DSPj; P r is to DSPi; D~ be the number of delegates committed to the the minimum fraction of vote which a candidate will candidate prior to DSP~; and f~ be the cost of allocating one day of campaigning to DSPj. In DSP~, let 8i be the receive if no time or money is spent in DSPj and no delegates have been in the previous primary; pj~ is the amount of funds allocated to advertising or other nonfraction of the vote a candidate will receive as a result of personal campaign activities; and r~ be the amount of winning ( D j - Dj-1) delegates in the most previous pripersonal campaign time allocated. Then let, Pi = p~(D~, 8~, r~) be the proportion of vote that the candidate mary; Pi2 is the fraction of the vote a candidate will wins given that he/she has previously won D~ delegates, receive for each unit of money spent in DSPj; P#3 is the spends 8~ dollars, and allocates ri time to DSP~; VC~(p~) fraction of the vote a candidate will receive for each day spent in DSPj; cr is the minimum contributions a canbe the number of delegates won in DSP~ if pi is the didate wiI1 receive if no votes were received in DSPj and proportion of the vote obtained; and Q(pi, D~) be the contributions received after DSP~ if D~ delegates have no delegates had been won previous to DSPj; cj I is the amount of contributions received for each fraction of the previously been won and p~ proportion of the vote is vote received; and cj2 is the amount of contributions obtained in DSP~. We then have the following optimizareceived for each delegate won in DSP's prior to DSP#. tion problem: We will also assume that the fraction of the vote a n candidate may receive is always less than some maximaximize D, = ~ W~(p~) (1) mum value, regardless of the time and money expended = and previous delegate won, i.e. subject to: d~+~= d~ - 8~- f F i + Q(PJ, Di), j = l , 2 . . . . . n - 1 (2) pj<-p~ (11) Dj+ 1=Dj-[-Wj(pj),
j = 1,2 . . . . . n - 1 (3)
] = 1,2
j = 1,2 . . . . . n
j = 1,2 . . . . . n
j = 1,2 . . . . . n.
In this formulation, (2) states that the money available to be spent in DSPj+t is equal to the money available for DSPj minus the amount spent in DSPi plus any contributions received after DSPj but before DSPj+~. The amount spent on DSPj includes spending for advertising (Sj) and money for personal appearances by the candidate (fF~). The value of &, the amount available before any campaigning may be assumed to be a known value. Constraint (3) states that the number of delegates won before DSPi+~ is equal to the number of delegates won before DSPj plus any won in DSP~. D~, the initial number of delegates won, is zero unless the model is being employed after the campaigning has begun. Constraint (4) restricts the time available for personal appearances prior to DSPj to the number of days remaining until DSPj. Constraints (5) and (6) restrict the amount of money spent on DSPi. (5) does this by not allowing more money to be spent than is available (di) while (6) restricts the legal level of spending to be less than a legal limit (8*). This legal limit will vary from state to state. Finally, (7) are the nonnegativity conditions one would expect for this problem. If we now assume that the functions Wj(.), Pj(.,., .) and Q(., .) are linear in their arguments, then (1)-(7) can
where p* is the upper limit on the fraction of the vote that may be obtained. Combining all of these expressions, we have the linear programming formulation: n
Maximize: D, = ~ ] w~pj*
subject to: pj = Pr + pj~(Dj - Dj_~) + Pj28j + pjaTb j = 1,2 . . . . . n (13)
j=l,2 ..... n-1
dj+~=dj-Sj-fFj+c*+cjlpa+cj2di, 1 =1 rk--
8i+fFj-d~O, 8~+hTj-< 6',
j=1,2 ..... n (15) n
j=l,2 ..... n /=1,2 ..... n
j=l,2 ..... n
d~,rj,6i, p~,Dj>-O, ] = 1 , 2 . . . . . n.
(16) (17) (18) (19) (20)
In (12)-(20), we have written the linear programming formulation of the primary allocation model. (12) and (14)-(20) are the linear version of (1)-(7) while (13) expresses the functional relation relating the percentage of votes, pj, to the decision variables. 3. AN EXAMPLE
As an example of this procedure, consider a three primary problem. For these primaries, the candidate and his/her advisors have forecast certain minimum and maximum values for percent of vote and contributions.
A financial planning model for presidential candidates These values along with total delegates, time available before each primary and maximum spending limits in each primary are shown in Table 1. We will also assume that the candidate has $300,000 to spend prior to Primary A. Note that in all three primaries, the candidate has a range of 50% between the minimum and maximum percentage of the vote that he/she can win. The marginal percentages are the amount for which allocations of spending and time must be made. Let us assume that the candidate has estimated the proportion of this marginal vote that depends upon spending, time, and prior victories. This information is shown in Table 2. In each case, the percentage shown would be won as a result of the maximum spending time, or delegates previously
The final parameters resulting from these c'. are shown in Table 3. Solving the linear programming problem whi, from using the values from Table 3 in (12)-(20)' the allocation shown in Table 4. If the allocations shown in Table 4 are used that 20 delegates will be won in Primary A, 77 will be won in Primary B, and 46 delegates will1 Primary C. This will give the candidate 143 which is almost a majority of the 300 delegates in the three primaries. In terms of percent of candidate will receive 40, 51.2 and 46.8% in pri~ B and C respectively.
Using Table 2, we may now calculate the parameters p~,, PJ2, PJ3. To calculate cj,, and c~2we will also assume that marginal contributions depend 40% on the most prior percent of vote won and 60% on the delegates won prior to the last election. The percentage based on spending, PJ2, is found by dividing the maximum spending percentage by the maximum spending level. The percentage based on time, PJ3, is found by dividing the maximum time percentage by maximum time available. Finally, the percent based on delegates, Pn is found by dividing the maximum delegate percentage by the maximum possible delegates. The percentage of donations based on prior percent of vote, cj1, is calculated by dividing 40% of the maximum marginal contribution by the percent of the vote in the most recent DSP. Also, the percentage of donations depending on delegates won, cj2, is found by dividing 60% of the maximum marginal contribution by the maximum possible delegates that could be won prior to the previous DSP.
4. SUMMARYANDCONCLUSIONS The necessity of entering state primaries and has greatly changed the nature of campaign making for presidential candidates. The fact t primaries and caucuses are highly interrelated rr resource allocation decisions made in early prirr not only affect the candidate's performance in mary but also will affect resources available performance in subsequent primaries. The nature of these allocation decisions and their e motivated the linear programming model pre this paper. In this model the objective
Table 4. Allocationsof time and money Advertising Spendin B $250,000 $ 1,182 $ 0
Table 1. Estimated values for primary example
Primary A B C
Index 1 2 3
Total Delegates 50
Time Available (Days) 14 21 28
Min ~ of Vote 20 30 10
Max of Vote 70 80 60
Maximum Min/Max Spendin 8 Delegates
$400,000 $500,000 $. . . . . . .
$250,000 $800,000 $600.000
10/35 45/120 JO/f~
$100,000 $200,000 $ .......
Days 14 21 2~
Table 2. Percentages of votes Primary A B C
Marginal ~ o f vote 50 50 50
Max time ~
Max Spending %
10 15 20
20 25 20
Table 3. Parameters for three primary example PJ 1 per Primary A B C
PJ 2 ~ per
PJ 3 ~ per
cj 1 $105,000
day .714 .714 .714
per .0629 .015 0
cj 2 $105,000 p e r
delesate 0 .0514 0
Campaigr Days 0.0 12.82 15.18
PATRICKCa.McKEoWNand ANDI~EWF. SEILA
represents the total delegates won in all primaries/caucuses entered and the constraints represent the relationships between resource allocations, percent of the vote received, contributions and time and money available, as well as limits on spending and time available. This model is primarily useful as a financial planning tool for campaign strategists. If it is applied in advance of the first primary, the optimal objective function value will indicate the number of delegates the candidate could win with the current initial level of resources (time and money). In addition the optimal values of the decision variables will assist advisors in planning the financial strategy of the campaign. The model could also be applied during the campaign to assist in re-evaluating the financial strategy as more definite information on contributions and resource levels becomes available. Sensitivity analyses permit assessment of the effectiveness of additional time and/or money resources. This would then provide a basis for decisions to borrow money or to initiate direct mail solicitations. The financial planning model discussed in this paper is an "aggregate" model in the sense that only spending and time allocation levels are determined by the model. The model does not indicate how much should be spent on different advertising media, nor when campaign appearances should be scheduled. Although one could refine the model to include provisions for alternative
allocations within each primary, we would suggest that this refinement might make the model less useful because the number of decision variables would be an order of magnitude larger. Instead, we would recommend that, in practice, once the level of spending is determined by the model in this paper, a separate model be applied to determine where efforts should be concentrated within the state and which advertising media should be used. Other refinements to the model might include a nonlinear objective function--perhaps piecewise linear--and also piecewise linear constraints to account for nonlinearities in delegates won and campaign contributions. Another aspect of the campaign environment that this model does not explicitly account for is competition from other candidates. This is in fact implicitly considered in the "upper limits on the percentage of the vote obtainable in each primary. Therefore, another direction for refinement might include modelling the strategies of other candidates. It is hoped that this model will not only free the candidate from some financial planning duties to concentrate on campaign issues, but also will stimulate other researchers to investigate the use of financial planning models in political campaigns. REFERENCES l. The New Republic 182, 11-13 (23 Feb. 1980). 2. Time 115, 16-17(3 Mar. 1980). 3. Time 115, 32 (14 April 1980).