The Ideological Incentive for Campaigning on Corruption Issues: The Two-Party Case

Abstract

In this chapter the theoretical model employed to identify the relationship between ideological positions and the incentives of a party to campaign on political corruption is introduced for a two-party system. The conclusion is that the more parties or candidates present a similar policy programme, the more such incentives grow. The empirical implications of the model are then controlled for by focusing on three countries: a ‘pure’ two-party system like the United States, and Italy and Japan during their respective long periods of no-cabinet alternation. Although these two latter democracies cannot be considered as two-party systems, they can be analysed using the theoretical framework proposed. Moreover, focusing on these two countries allows deeper investigation of the negative side of valence campaigning on corruption by a perennial opposition party.

Appendices

Appendix 1: Quadratic vs. Linear Utility Loss

Spatial models conceptualize individual utility over a particular alternative as maximized when the location of that alternative is identical to an individual’s ideological ideal point. Utility decreases as the distance between the alternative and the individual’s ideal point increases. That is, each individual’s preference curves are single-peaked and slope downward monotonically from the point of highest utility. While the idea that voters are more likely to support a party that largely shares their own preferences seems intuitive, and has served as a starting point for numerous studies on voting behaviour, scholars have devised different ways to capture how much weight citizen-party ideological proximity carries. Some researchers conceptualize the monotonic utility decrease as a linear function: for every increase of one unit in this distance, voters lose one unit’s worth of benefit, or utility (Blais et al. 2001; Krämer and Rattinger 1997; Wessels and Schmitt 2008). In this case, the utility i that derives from choosing party A can be represented as follows: U _i = − |x _i − A|. Linear loss implies that as ideological distance increases, utility decreases at a uniform rate; a shift from a deviation of 0 units to 1 unit will affect the utility to the same extent as a shift from a deviation of 2 units to 3 units. In this sense, such function identifies actors that are risk-neutral (i.e. they face constant marginal losses). Other authors propose a quadratic relationship: for every increase of one unit in ideological distance, voters lose the square term of one unit’s worth of utility (Calvo and Hellwig 2011; Duch et al. 2010; Jessee 2010; Curini et al. 2015). This also means that such a quadratic loss ‘penalizes’ distant alternatives (those beyond 1 unit) at an increasing rate by squaring the deviations from one’s ideal point. To resume the previous example, the quadratic utility loss (used in Sect. 2.1 to derive Eq. (2.3)), would be for i: U _i = − (x _i − A)². For example, a shift from a deviation of 0 to a deviation of 1 unit will still register as a loss of ‘1’, while a shift from a deviation of 2–3 units will register as a loss of ‘5’ (3² − 2² = 5).

As already discussed in Sect. 2.1, the interpretation of a quadratic loss function is that actors are risk averse (i.e. they face increasing marginal losses), an assumption commonly made in the literature on spatial voting (Calvo and Hellwig 2011; Adams et al. 2005). Other authors, however, consider a linear loss function to be a better representation of human (and therefore voters’) behaviours (Hammond and Summers 1965; Hastie and Dawes 2010; Singh 2014).

Employing a linear loss function would imply some changes in the theoretical framework discussed in Sect. 2.1. In particular, Eq. (2.2) in Sect. 2.1 (i.e. the electors’ utilities to vote for L and R given a valence advantage for party L equal to k) would become:

$$ {u}_L(z)= k\hbox{--} a\left| x\hbox{--} z\right|,\kern0.875em {u}_R\left(\mathrm{z}\right)=\hbox{--} a\left| x+ d- z\right| $$

(2.4)

By equalizing u _L (z) and u _R (z) in Eq. (2.4), to find the location of the indifferent voter, three possible situations can be envisaged:

• (a) when $d>\frac{k}{a}$, the increase in votes for L following a successful move in valence issues (i.e. producing k > 0 ) is $\frac{k}{2 a}$, independently of the distance between party platforms;

• (b) when $d>\frac{k}{a}$, party L takes all votes and party R obtains none;

• (c) similarly, when both parties share a similar platform, i.e. when d ≈ 0, any valence surplus of party L is sufficient to gain all votes.

Now, if it is admitted—as discussed earlier—that a valence campaign (i.e. the ability to produce k > 0) is costly, so that it is undertaken inasmuch as its expected benefits are huge, then the previous analysis at point (c) suggests that the opportunity to obtain a large(r) success in terms of votes through a successful valence campaign increases with the proximity between the platforms. Thus, exactly as happens with the quadratic loss function discussed in Sect. 2.1, one may conjecture that in a two-party system, a party envisages an inverse functional relation between the ideological distance from the rival and the incentive to engage in valence campaigning.

Note that point (c) above requires that the two parties share exactly the same position. This hypothesis can be relaxed by moving from a deterministic to a probabilistic voting model. In this latter case (see, for example, Chappell and Keech 1986), the general assumption is that the probability that parties ascribe to the vote of an elector with ideal point z depends on |x − z| − |a + d − z|, i.e. the difference of the distances between z and the parties’ locations on the left-right continuum. The closer this difference (i.e. the lower the value of d), the lower such probability becomes and vice-versa. Intuitively, this happens because the ability of voters to differentiate among parties’ locations in the policy space is also inversely related to d, given that the amount of (costly) information that voters would need to acquire to correctly differentiate parties’ locations when d is low increases substantially. But if that is true, then condition (c) above would hold also for values of d larger (although not substantially larger) than 0, given that in those situations for a voter the ‘perceived d’ would be almost 0. This should increase the incentives for a party to invest in a valence campaign, notwithstanding the fact that the ‘real d’ could be different (although not that much different) from 0.

Appendix 2: Policy vs. Valence Weight

Figure 2.4 in Sect. 2.1 illustrates party L’s incentive to campaign on valence as a function of the distance d between L and R. Note that, if I take the changing slope of party L’s incentive to play valence with respect to the distance between parties (i.e. ∂² U _L /∂k∂d = −1/2ad ²) as a measure of party L’s responsiveness to distance variation, then, by acknowledging that the hyperbola 1/2ad meets its axis of symmetry when the distance between parties is $1/\sqrt{2 a}$, I can derive that the critical distance where the hyperbola reaches its maximum curvature, and its slope is −1 as the ‘spatial divide’ between the zone where the incentive to campaign on valence issues is strong, although in a rapidly decreasing way, and the zone where that incentive begins to be more and more indifferent to valence competition and flatly decreases toward 0.

Moreover, because that critical distance depends inversely on a, it can be added to this conclusion that the higher the relative salience of the ideological competition with respect to L’s capacity to satisfy the electors’ preference for socially shared values, the smaller is the range of d where valence issues may play a significant electoral role. Conversely, the less parties’ electoral success is influenced by their ideological distance, the larger is the spatial range where valence campaigning will be rationally adopted. Figure 2.8, where two curves for two values of a (a´ > a˝) are plotted, illustrates the content of this paragraph.

Fig. 2.8

Party L’s incentive to compete on valence depends on the variable d and on the parameter a

Note, however, that d and a are not independent from each other. According to the literature, the strength of policy or ideological voting (i.e. the value of a) increases with the degree of party system polarization (i.e. a measure that is inversely related to d; see Chap. 5) (Alvarez et al. 2000; Kroh 2009; Lachat 2008). With parties spread across the ideological spectrum, in fact, it may be easier for voters to identify differences among parties and thereby to select a party closer to their own views (Dalton 2010). This should increase the salience of policy as a function of party system polarization. ¹ These arguments are coherent with the findings highlighted in several empirical papers (Ensley 2007; Green 2007; Green and Hobolt 2008), where it is shown that when candidates minimize their ideological distance, the salience of ideology (which in the model is measured by the a parameter) decreases in voters’ decisions and in candidates’ campaigning.

These findings are a good news for the present study. In fact, in the empirical analyses I never estimated a directly. Given what was noted just above, however, this can be somehow ‘safely’ neglected given that the value of a should change in the same direction of d.

Note

• 1. See Curini and Hino (2012) for a different perspective in this regard.

Appendix 3: Extracting Party Left-Right Scores from CMP Dataset

As discussed in Sect. 2.1, the CMP database takes 13 categories as indicators of policy positions representing the ‘left’ and another 13 as indicators of policy positions representing the ‘right’. The basis of the selection of such 26 categories is mainly theoretical: highly influential early modern theorists put them together in their political analyses. Left categories are linked in Marxist and progressive political analyses of around 1900, and contrast with right topics linked together in opposing analyses broadly supporting the existing order and market (Budge et al. 2001). Table 2.4 reports the list of these 26 categories together with the CMP denominations. ¹

Table 2.4 The 26 CMP categories used to estimate a left and a right position

Moving from these 26 categories to a left-right score for a party has produced a wide debate in the literature. As discussed in Sect. 2.2, I have adopted the method originally proposed in Budge and Laver (1992), which still represents the benchmark when dealing with CMP data: in this case, the left-right position is constructed for each party in each election by subtracting the sum of its left statements from the sum of its right statements. In terms of raw numbers of quasi-sentences ² coded into each category (rather than their percentage), it can be written as:

$$ \mathrm{Left}\ \mathrm{Right}\left(\mathrm{difference}\right)=\left( R- L\right)/\left( R+ L+ O\right)=\left( R- L\right)/ N, $$

(2.5)

where O refers to the ‘other 30 categories’ included in the CMP dataset but not in the 26 categories used to build a left-right position. This measure is therefore based on the difference in counts between left and right sentences normalized by the total number of sentences in the manifesto on any issue. Note that according to Eq. (2.5), counts of the categories not in the scale (i.e. O) still affect estimated party positions, so that it can happen that a party may be scored as less right-leaning (or left-leaning) by virtue of devoting more attention to topics that are not purely left or right (i.e. by increasing the value of O). The underlying assumption is that if an issue becomes less important, then a party will devote fewer sentences to it. This can be justified on the grounds that programmes are not just a compilation of discrete policy stands but integrated and complete statements all of whose constituent parts have been carefully considered in relation to each other by programme committees and party conventions and approved as a whole by the latter.

A first proposed alternative to Eq. (2.5) is to normalize the left-right scores estimated with the salience that each party assigns to the categories comprising the left-right scale as follows:

$$ \mathrm{Left}\ \mathrm{Right}\left(\mathrm{ratio}\right)=\left( R- L\right)/\left( R+ L\right) $$

(2.6)

The measure originally proposed by Kim and Fording (1998) ranges from −1 to 1 (rather than from −100 to 100 as in the Eq. (2.5) case) and makes the range constraint hidden in that measure explicit. Dividing by R + L decouples the measure from variation in the importance that a party assigns to any issue area (other than R and L). As a result, this measure will not necessarily create an apparent move to a more centrist position if the party decides to focus on other policy areas (given that O is not considered contrary to Eq. (2.5)). However, under some circumstances, Eq. (2.6) could force the left-right scores to the extremes, i.e. generating a score of −1 when R = 0 irrespective of the value of L, or to 1 when L = 0 irrespective of the value of R, leading to spikes at the boundaries of the scale.

A more recent alternative to Eq. (2.5) has been advanced by Lowe et al. (2011). In this case, the authors suggest focusing on the relative balance between quantity of sentences, or R/L. Note that by doing so, the marginal effect of one more quasi-sentence is decreasing in the amount that has already been said on the topic. For example, compare two situations: in the first one, the party’s previous platform contained 50 right-leaning sentences, and 20 left-leaning ones, then a new manifesto containing 50 right-leaning sentences and 21 left-leaning ones; in the second situation, the previous platform had contained 10 and 4 right and left-leaning sentences, and the new platform 10 and 5. The effect of adding one more sentence in the first case decreases the right-left ratio sentences by about 5% (50/20 = 2.5; 50/21 = 2.38; (2.38/2.5) − 1 = −5%), and in the second by 20% (10/4) = 2.5; 10/5 = 2; (2/2.5) − 1 = −20%). As a result, the left-right score of a party should be obtained by operating in proportions and working with a logarithmic scale relationship between the underlying quantity and subjective estimations of it. ³ That is:

$$ \mathrm{Left}\ \mathrm{Right}\left(\mathrm{logit}\right)= \log \left[\left( R+0.5\right)/\left( L+0.5\right)\right] $$

(2.7)

Despite their underlying differences, the three measures produce actually very similar results. ⁴ The correlation in the entire CMP dataset between Eqs. (2.5) and (2.6) is .957; between Eqs. (2.5) and (2.7) is .949.

Not surprisingly, therefore, if I replicate, for example, the analysis in the US case (see Sect. 2.2) by using the Eq. (2.6) or (2.7), the results are remarkably similar to the estimates that I obtain by using the Eq. (2.5) measure. See Table 2.5 in this respect.

Table 2.5 Explaining CORRUPTION in the US case according to SPATIAL PRESSURE (using alternative estimations of party left-right scores from CMP data)

Notes

• 1. See https://manifesto-project.wzb.eu/ for a detailed discussion of the meaning of each category.

• 2. A quasi-sentence is the coding unit employed in the CMP codification stage, i.e. the part of a text that contains exactly one statement. This also implies that in a given sentence, there may be more than one single quasi-sentence.

• 3. Using a logarithmic scale implies that exponentially more sentences in L or R are needed to move the policy position of a party toward an extreme position. The addition of 0.5 to Eq. (2.7) helps to make position estimates created from very small counts more stable.

• 4. An alternative approach to estimation of left-right scores for parties by employing CMP data is proposed by Gabel and Huber (2000). In their case, the left-right dimension is defined as the ‘super issue’ that most constrains parties’ positions across a broad range of policies. More in detail, they propose the use of factor analysis to extract the latent dimension that best accounts for the observed covariation across parties among all the categories in the dataset and treat it as the effective ideological dimension along which parties compete. See Curini and Martelli (2015) and Curini (2015a) for an application of this method in the case of valence campaigning with, respectively, CMP and legislative speeches data.