The poll results hypothesis.

Introduction

Since Downs (1957) introduced the theory of the "rational voter," there have followed numerous and highly varied theoretical extensions and empirical studies to enhance, test, and better understand the theory or variants thereof in a variety of "real world" and "experimental"

frameworks (e.g., Aldrich 1993; Aldrich & Simon 1986; Ashenfelter & Kelly 1975; Barreto, Segura & Woods 2004; Borgers 2004; Brazel & Silberberg 1973; Cebula 2001; Cebula 2004; Cebula & Kafoglis 1983; Copeland & Laband 2002; Cox & Munger 1989; Feddersen 2004; Greene & Nikolaw 1999; Green & Shapiro 1994; Kafoglis & Cebula 1981; Knack, 1999; Lapp, 1999; Ledyard, 1984; Leighly, 1996; Morton, 1987; Mueller, 2003; Piven & Cloward 1988; Putnam, 2000; Riker & Ordeshook 1968; Schram, 1992; Schwartz, 1987; Teixeira, 1992; Tullock, 1967; Verba, Schlozman, & Brady 1995; Wolfinger & Rosenstone 1980).

The complexities involved in voting behavior and the voting process are doubtless best exposed in the classic works by Buchanan and Tullock (1962) and Tullock (1967). Moreover, the possibility of voting in alternative ways, such as "voting with one's feet," is exemplified in the works of Tiebout (1956) and Tullock (1971), among others. The hypothesis of "voting by tax evasion" has been introduced by Cebula (2003), whereas Copeland and Laband (2002), and to a significant degree, Barreto et al., (2004) and Cebula (2004), have empirically investigated a theory of" expressive voting." To some extent, Cebula (2003) on the one hand and Barreto et al., (2004), Cebula (2004) and Copeland and Laband (2002), on the other hand, respectively, represent efforts either to identify nontraditional ways in which to vote vicariously and/or to introduce non-traditional and/ or non-demographic variables that may explain voting behavior.

Dismay and concern regarding both low and declining voter participation rates in the U.S. are expressed frequently in the media and elsewhere. In the words of Putnam (2000, p. 31), "With the singular exception of voting, American rates of political participation compare favorably with those in other democracies..." Putnam (2000, p. 31) proceeds to observe "We are reminded each election year that fewer voters show up at the polls in America than in most other democracies..." Putnam (2000, p. 32) further observes that "Turnout has declined despite the fact that the most commonly cited barrier to voting ('burdensome registration requirements') has been substantially lowered."

The primary objective of this study is to expand the rational voter model (RVM) to reflect consideration of the results of polls of likely voters' Presidential candidate preferences. In particular, this study seeks to test the following hypothesis (labeled here as the poll results hypothesis): in any given state, given the existence of the Electoral College system, the greater the lead of a principal Presidential candidate over his/her closest rival as revealed in polls of likely voters, the lower, for at least some portion of prospective voters, the expected gross benefits from voting in that state and hence the lower the aggregate voter participation rate in that state. There are at least two dimensions to this hypothesis. First, if one's own preferred principal candidate is revealed as leading by a "comfortable" or "statistically significant" margin according to the poll of likely voters in one's own state, the benefits one expects from actually voting may be diminished. This is because the poll indicates that more than enough votes are likely to be cast in the state for that candidate to ensure his/her carrying that state in the Electoral College tally. Indeed, the greater the lead enjoyed in the poll by one's preferred candidate, the lower the expected benefits from one's voting and hence the lower the probability that one will actually show up at the voting booth. This implies a reduction in the aggregate voter participation rate in the state as a consequence of these poll results. Second, if one's own preferred principal candidate is revealed as trailing by a "substantial" or "statistically significant" margin according to the poll of likely voters in one's own state, then the benefits one expects from voting may also be diminished. This is because the poll indicates that more than enough votes are likely to be cast for the opposing candidate to ensure his/her carrying that state in the Electoral College. In this scenario, one could very well perceive voting as a "wasted effort" or "futile exercise" since the outcome may already be a de facto foregone conclusion. Once again, the implication is a reduced aggregate voter participation rate in the state due to these poll results.

The following section of this study provides the model to be examined. The subsequent section provides the empirical model and the empirical findings. Finally, the concluding section provides a summary of the model and the empirical findings, along with certain potential implications thereof.

The Framework

Paralleling in principle the RVM, it is hypothesized that the probability that a given eligible voter will actually vote, PROBE is an increasing function of the expected gross benefits (EGB) associated with voting, ceteris paribus, and a decreasing function of the expected gross costs (EGC) associated with voting, ceteris paribus. Thus, it follows that:

PROBV = f(EGB, EGC), [f.sub.EGB] > 0, [f.sub.EGB] < 0; [f.sub.(EGB - EGC)] > 0 (1)

The central hypothesis to be investigated in this study is what is referred to above as the poll results hypothesis. This hypothesis is explained in general terms in the Introduction. However, since this study seeks to provide current/contemporary empirical insights, it focuses on the 2004 Presidential election. Accordingly, the poll results hypothesis focuses in this study on the two leading/principal candidates for President in each state in 2004, George Bush and John Kerry. Within the framework of the 2004 election and within the context of the Electoral College system, it is argued that, within any given state, the greater the lead of George Bush over John Kerry, as revealed in the poll of likely voters in that state, the lower, for at least some portion of prospective voters, the expected gross benefits of voting, EGB, in that state. According to the poll results hypothesis, at least some percentage of the supporters of both candidates in the state expect reduced benefits from their voting. On the one hand, the greater the lead in the poll for George Bush over John Kerry in the state, the less the degree to which at least some George Bush supporters expect their votes to be necessary to their preferred outcome. That is, given the context of the Electoral College, the greater George Bush's lead in the state (according to the poll), the less the need for his supporters to vote in order to secure the state in the Bush victory column. Ergo, the voter turnout among Bush supporters is expected to be lowered since at least some percentage of them expects their votes to yield lower, possibly even zero, net benefits. Moreover, the greater George Bush's lead in the state (according to the poll), the lower, for at least some portion of John Kerry supporters, the expected benefits of voting in that state. That is, from a practical viewpoint, their votes would be expected to very likely yield low (and possibly even zero) net benefits since the poll results imply a high probability of victory for Bush. These lowered expected benefits from voting in the state are expected to further reduce the state's voter turnout.

Consequently, it is hypothesized, among those states where Bush votes (BV) are revealed (in polls of likely voters) to outnumber Kerry votes (KV), that the greater the ratio of BV to KV in any given state, the lower the aggregate voter participation rate (VPR) will be in that state, ceteris paribus. Similarly, the poll results hypothesis argues that among states where polls of likely voters reveal that KV>BV, the greater the ratio of KV to BV in any given state, the lower the VPR will be in that state, ceteris paribus.

Naturally, other factors influence the expected benefits and costs of voting in a state. Presumably, the greater the education level, the greater may be the public's awareness of the importance and relevance of voting in maintaining a free society. To proxy educational attainment, we adopt the percentage of the adult population (age 25 and above) with at least a high school diploma, HS. Thus, it is hypothesized that the voter participation rate in a state, VPR, is an increasing function of HS in that state, ceteris paribus. It has often been found in the literature that blacks in the U.S. have a lower voter participation rate than most other demographic groups. A possible partial explanation for this finding may be that the expected benefits from participation in the election process may be lower fur blacks than for most other demographic groups, perhaps because of experienced disappointments with previous election participations or perhaps as a reflection of feelings of being disenfranchised from the mainstream political system ([Putnam (2000), p. 32]). In any event, it is hypothesized here that the VPR in a state is a decreasing function of the percentage of the total population in the state that is black (PCTBL), ceteris paribus. According to both Cebula (2004) and Copeland and LaBand (2002) voters often vote to express how they feel, be it on social, political, economic, or other issues. For example, [Cebula (2004), p. 219] finds people often wish to express their dissatisfaction with government over higher unemployment rates. Consequently, it is hypothesized here that the VPR in a state is an increasing function of the unemployment rate (UR) in the state, ceteris paribus. Finally, higher levels of median family income (MFI) increase the expected gross costs (EGC) of voting by raising the opportunity costs associated with voting. Accordingly, the VPR in a state is expected to be a decreasing function of the state's MFI, ceteris paribus.

Substituting for EGB and EGC in Eq. 1 yields, for states where BV>KV:

PROBV = f(BV/KV, HS, PCTBL, UR, MFI),

where: [f.sub.BV/KV] < 0, [f.sub.HS] > 0, [f.sub.PCTBI] < 0, [f.sub.UR] > 0, [f.sub.MFI] > 0 (2A)

On the other hand, for states where KV>BV, the specification becomes:

PROBV = g (KV/BV, HS, PCTBL, UR, MFI),

where: [g.sub.KV/BV] < 0, [g.sub.HS] > 0, [g.sub.PCTBL] < 0, [g.sub.UR] > 0, [g.sub.MFI] < 0 (2B)

Predicated upon the frameworks expressed in Eqs. 2A and 2B, the model of aggregate voter participation rates at the state level involves estimating reduced-form Eqs. 3A and 3B, respectively:

[VPR.sub.j] = [a.sub.0] + [a.sub.1] [(BV/KV).sub.j] + [a.sub.2][HS.sub.j] + [a.sub.3][PCTBL.sub.j] + [a.sub.4][UR.sub.j] + [a.sub.5[MFI.sub.j] + u (3A)

[VPR.sub.j] = [b.sub.0] + [b.sub.1][(KV/BV).sub.j] + [b.sub.2][HS.sub.j] + [b.sub.3][PCTBL.sub.j] + [b.sub.4][UR.sub.j] + [b.sub.5[MFI.sub.j] + u' (3B)

where:

[VPR.sub.j] = the aggregate voter participation rate in state j in the 2004 general election, expressed as a percent;

[a.sub.o], [b.sub.o] = constant terms;

[(BV/KV).sub.j] = the ratio of the percentage of likely voters in state j who would cast their vote for George Bush in the November, 2004 election to the percentage of likely voters in state j who would cast their vote for John Kerry in that election, based on state-level polls of likely voters;

[(KV/BV).sub.j]= the ratio of the percentage of likely voters in state j who would cast their vote for John Kerry in the November, 2004 election to the percentage of likely voters in state.] who would cast their vote for George Bush in that election, based on state-level polls of likely voters;

[HS.sub.j] = the percentage of the population in state j age 25 and above with at least a high school diploma, 2003;

[PCTBL.sub.j] = the percentage of the total population in state j that was black, 2003;

[UR.sub.j] = the percentage of the civilian labor force in state j that was unemployed, 2003;

[MFI.sub.j] = median family income in state j for a four person family, 2003;

u, u' = stochastic error terms.

The study deals exclusively with the 50 states during the 2004 general election in the U.S.; Washington, D.C. was not included in the study. The [VPR.sub.j] data were obtained from: http://www.uselectionatlas.org/USPRESIDENT/vto.php? year=2004&datatype=national. The data for [HS.sub.j], [Ur.sub.j], and [PCTBL.sub.j] were obtained from the [U.S. Census Bureau 2004-2005, Tables 216, 610, 21]. The data source for the variable [MFI.sub.j] was http://www.census.gov/hhes/income/4person.hunl. The source for variable (BV/KV)j was http://www.americanresearchgroup.com/ec2004/.

Empirical Findings

In order to empirically test the poll results hypothesis in the framework outlined above, two OLS estimates are offered. In both estimates, which are provided in Table 1, the White (1980) procedure for heteroskedasticity correction has been applied. In column (a) of Table 1, the model in Eq. 3A is estimated for only those states (30) in which George Bush held a lead over John Kerry in the polls of likely voters, whereas in column (b) of Table 1, the model is estimated only for those states (20) in which John Kerry held a lead over George Bush in the polls of likely voters.

In column (a) of Table 1, the estimated coefficients on all five of the explanatory variables exhibit the hypothesized signs, with one significant at the 1 percent level, one significant at the 2.5 percent level, and two significant at the 10 percent level. The coefficient of determination is 0.63, so that the model explains nearly two-thirds of the variation in the voter participation rate by state. The F-statistic is significant at well beyond the 1 percent level, attesting to the overall strength of the model. In column (b). four of the five estimated coefficients exhibit the extpected signs, but in this estimate two coefficients are significant at the 1 percent level, one is significant at the 5 percent level, and one is significant at the 10 percent level. The [R.sup.2] is 0.89, so that in this case the model explains nearly nine-tenths of the variation in the VPR. Finally, the F-statistic is significant at tar beyond the 1 percent level, attesting once again to the strength of the model as a whole.

The estimated coefficient on the HS variable is positive and significant at the 1 percent level in both estimates. Thus, as hypothesized, it appears that a greater degree of education acts to elevate voter participation, perhaps because the education creates awareness of the importance of voting in a democratic system. The coefficient on the PCTBL variable is negative in both estimates, as hypothesized, but statistically significant (at the 1 percent level) only in the estimate corresponding to Eq. 3B. This finding, in terms of Eq. 3B, would appear to reflect the commonly found result that blacks have a lower voter participation rate than most other demographic groups, perhaps based on historical experiences that create the perception of a small benefit to be realized from voting ([Putnam, 2000, p. 32]). In Table 1, only one of the two coefficients on the UR variable is positive; moreover, this single coefficient is significant at only the 10 percent level. Thus, there is only weak evidence that the public voted in 2004 to express their feelings/concerns over higher unemployment rates per se (Barreto et al., 2004; Cebula, 2004; Copeland & Laband 2002). The estimated coefficient on the MFI variable is negative in both estimates, as hypothesized, and significant at the 10 percent level in both cases as well; thus, there is modest evidence that a higher median family income reduces voter turnout, arguably because of opportunity cost considerations. Finally, consistent with the hypothesized signs provided in Eqs. 2A and 2B, respectively, the estimated coefficient on the BV/KV variable in column (a) for Eq. 3A is negative and statistically significant at the 2.5 percent level, whereas the coefficient on the KV/BV variable in column (b) for Eq. 3B is negative and statistically significant at the 5 percent level. Thus, there is strong empirical evidence on behalf of the poll results hypothesis. Accordingly, based on state-level poll results of likely voters, it appears that the greater the lead in any given state that either of the two front-running Presidential candidates holds over the other, the lower the expected gross benefits (EGB) of voting in that state and therefore the lower the aggregate voter participation rate in that state.

Conclusion

This study introduces the poll results hypothesis. According to this hypothesis, in any given state, within the context of the Electoral College system, the greater the lead of a principal Presidential candidate over his/her closest rival, as revealed in polls of likely voters, the lower, for at least some portion of prospective voters, the expected gross benefits from voting in that state and hence the lower the aggregate voter participation rate in that state. Stated in different terms, free riding among voters is encouraged in those states where either of the principal Presidential candidates is revealed to hold a non-trivial lead, i.e., a statistically significant lead, in the poll of likely voters. An empirical analysis of the 2004 general election involving candidates George Bush and John Kerry provides strong empirical support on behalf of the poll results hypothesis.

Indeed, although such an analysis is beyond the scope of the present study, the hypothesis might well in effect be applicable to alternative contexts. Consider, for instance, the potential negative impacts on voter turnout of polls of likely voters taken in regard to cases involving two principal candidates for state-level offices and/or two principal candidates for "key" local offices (perhaps especially in non-Presidential election years) when such polls show a "large" margin between the leading candidates; conversely of course, if the polls show a very small margin between the leading candidates, the poll results hypothesis, properly interpreted, would imply a greater voter turnout! Indeed, even voter turnout for referenda and initiatives (in those states where such issues reach the voting booth) could be affected by the polls of likely voters.

Finally, the poll results hypothesis [and, arguably, the empirical evidence on behalf of same in columns (a) and (b) of Table 1, carefully interpreted] yield an interesting implication in addition to those already stressed in this study. Namely, as the ratio (BV/KV)j or, equivalently, (KV/BV)j, approaches unity, the incentive to free ride declines to its minimum and the incentive to vote increases to its maximum, ceteris paribus:

lim [VPR.sub.j] = MAXIMUM [(BV/KV).sub.j][right arrow] 1 (4)

This suggests, if one plots the ratio (BV/KV) [or the ratio (KV/BV)] along the abscissa and the VPR along the ordinate axis, that the VPR reaches its maximum at the point where BV/KV [or KV/BV] attains a value of 1. An alternative expression of this notion is that, given the nature of the "winner-takes-all" rule in each state under the Electoral College system, the VPR is maximized where BV/KV is approximately 1 because the election in that state then de facto becomes a "small numbers case."

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Published online: 6 January 2007

Richard J. Cebula ([mail envelope]) * Daniel Hulse

Armstrong Atlantic State University, Savannah, GA, USA

e-mail: cebulari@mail.armstrong.edu

Table 1 Alternative Estimates
of the Poll Results Hypothesis

                      Variable/Estimate     (a)           (h)

                      [(BV/KV).sub.j]      -4.98 ***
                                          (-2.38)
                      [(KV/BV).sub.j]                    -2.83 **
                                                        (-2.09)
                      [HS.sub.j]           +1.71 ****    +1.89 ****
                                          (+6.50)       (+6.79)
                      [PCTBL.sub.j]        -2.60        -36.01 ****
                                          (-0.33)       (-8.25)
                      [UR.sub.j]           +1.62 *       -0.37
* Statistically
significant at the                        (+1.76)       (-0.40)
10 percent level      [MFI.sub.j]          -0.0002 *     -0.0001 *

** Statistically
significant at the                         (-1.75)      (-1.93)
5 percent level       n                     30           20

*** Statistically
significant at the    [R.sup.j]              0.63         0.89
2.5 percent level     adj[R.sup.j]           0.56         0.85

**** Statistically
significant at
the 1 percent level   17-statistic           8.48 ****     23.23 ****