2.1 Data

We compile a dataset comprised of elections in OECD member countries in Europe, North America, and Asia from 1945 to 2015. Each country enters the panel in its first post-war democratic election. Our dependent variables are coded from the Manifesto Project's (MARPOR) right-left coding of party platforms (Lehmann et al., Reference Lehmann, Matthieß, Merz, Regel and Werner2016).Footnote ³

Our main sample comprises all parties whose platforms are coded by MARPOR during this period.Footnote ⁴ We ask how the electoral performance of governing parties relates to changes in party platform, focusing on three measures constructed from the right-left coding of platforms. Denote MARPOR's right-left coding (RILE) as $P_{t}^{ic}$ on for party i in country c's platform in the election t. This coding ranges from − 100 (leftmost) to 100 (rightmost). First, we examine the magnitude of ideological shifts, a standard measure of platform movement between elections. In Equation 1, Shift Magnitude _it is calculated as the absolute value of the difference in platforms:

(1)$${Shift\, Magnitude}_{it} = \vert P_{t + 1}^{ic}-P_{t}^{ic}\vert $$

A second outcome measures the direction of shifts in platform between consecutive elections, classifying ideological shifts as movement to the center or the extreme. In order to measure such shifts, we categorize parties as “left” or “right.” To maintain consistency, we examine whether a party's mean right-left platform ideology is left or right of zero. A party with a mean ideology less than zero is classified as a left party while a party with a mean ideology to the right of zero is classified as a right party.Footnote ⁵ Define the resultant set of left parties as ${\cal L}$ and the set of right parties as ${\cal R}$. The measure of shifts to the extreme is thus calculated as per Equation 2. This measure is positive when parties shift to the extreme between elections t and t + 1 and negative when parties shift to the center between elections t and t + 1. This variable thus measures shifts toward the extremes of the unidimensional policy space.

(2)$${To\, Extreme}_t^{ic} = \left\{\matrix{ P_{t}^{ic}-P_{t + 1}^{ic} \hfill & \rm{if} \,i \in {\cal L}\hfill \cr P_{t + 1}^{ic}-P_{t}^{ic} \hfill & \rm{if} \,i \in {\cal R} \hfill }\right.$$

The final dependent variable is a categorical classification of left, right, and center platforms. While parties are unlikely to run on both left and right platforms in different elections over time, there is substantial temporal variation in whether a party runs on a left (resp. right) or center platform. We classify each platform relative to the distribution of platforms from that country over the duration of the panel. Denote the country mean for each country's distribution of platforms as $\mu _{P^c}$ and the country standard deviation of these platforms as $\sigma _{P^c}$. Center platforms are those within half of the country-specific standard deviation in either direction of the country mean. Left platforms fall below this range while right platforms fall above this range. Formally, this classification is described by Equation 3. We probe the robustness of all results to the choice of bandwidth of the center category, as well as to different normalizations of platforms.

(3)$${Platform\, classification}_{t}^{ic} = \left\{\matrix{ \rm{Left} \hfill & \rm{ if} \;P_{t}^{ic} < {\it \mu}_{\it P^c} - {1\over 2} \it \sigma_{P^c}\hfill \cr \rm{Center} \hfill & \rm{ if} \;P_{t}^{ic} \in [ {\it \mu}_{\it P^c} - {1\over 2} {\it \sigma}_{\it P^c},\; {\it \mu}_{\it P^c} + {1\over 2} {\it \sigma}_{\it P^c}] \hfill \cr \rm{Right} \hfill & \rm{ if} \;P_{t}^{ic} > {\it \mu}_{\it P^c} + {1\over 2} \it \sigma_{P^c}\hfill \cr \hfill }\right.$$

Our main treatment variable is a binary indicator of whether a governing party loses power in an election in election t. To create this variable, we determine the governing party prior and subsequent to each election. If these parties change, the indicator is coded as a loss of power for the party governing prior to the election. We avoid classifying caretaker government parties as the “governing” party by looking at the party in power six months prior to the election (or the last government not denoted a caretaker government). This variable was hand-coded then compared to the Seki–Williams dataset on governments to assess the accuracy of the coding (Williams and Seki, Reference Williams and Seki2016). We additionally record whether or not the party was governing in a coalition, allowing us to examine the robustness of results to any ambiguities in identifying the governing party within coalition governments. In the US, the government coding corresponds to the presidency.

Empirically, there exist various paths to a loss of power. We emphasize the role of electoral defeat, yet the mapping between electoral returns and loss of power varies across the elections and countries in our sample. Most obviously, the translation of votes into defeat varies with electoral and political institutions. Our goal empirically is to start from the most general definition of loss of power within the full sample of countries and elections. We then report ancillary specifications documenting limited heterogeneity across electoral institutions which provide evidence in favor of the generality of our results.

We focus on the internal structure of parties and how party leadership is selected as a key moderator variable. This moderator is operationalized as the comparative size of the “selectorate,” or the body that selects the party leader. We utilize data assembled by Kenig et al. (Reference Kenig, Rahat and Hazan2013) on the relative size of the selectorate, and extend their data by adding additional countries. Our original coding is based on country-specific accounts such as Cross and Blais (Reference Cross and Blais2012), in addition to news articles on the selection of party leaders. Given the time period of the original dataset and difficulties in locating earlier information, we focus on the post-1960 era.Footnote ⁶ We code parties as having a large selectorate if party leadership is selected by a party convention or a body implying broader participation such as an open or closed primary. A small selectorate is defined as selection by a body smaller than the party convention, including a party council (smaller than a convention), a parliamentary caucus, or a single individual.

2.2 Estimation

Our empirical specifications are estimated using weighted ordinary least squares. Each country is weighted by the inverse of its proportion of total observations, effectively affording equal weighting by country.Footnote ⁷ We estimate Equation 4, in which β₁ is the estimator of the association between the main exposure variable, Loss of Power_it, and party positioning outcome, Y _ict.

Here, outcomes are indexed by party (i), country (c) and election (t) or decade (d). A set of covariates X_ict aims to control linearly for variables that are correlated with but qualitatively different from loss of power. To that end, we include vote share in election t, and a binary indicator for coalition status prior to election t in all specifications. We present summary statistics on these variables in Appendix A3 and describe the coverage of the panel in Appendix A11. We also include party fixed effects κ_i (as denoted) and election fixed effects (γ_t) in different specifications. In Appendix A8, we demonstrate the robustness of our findings to mean partisan ideology (prior to the election at time t) controls following Ezrow et al. (Reference Ezrow, De Vries, Steenbergen and Edwards2011). In all specifications, we cluster standard errors at the level of the party.

(4)$$Y_{ict} = \beta_1\ \rm{Loss \, of \, Power}_{it} + {\boldsymbol \psi}{\bf X}_{ict} + {\boldsymbol \gamma}_t + {\boldsymbol \kappa}_i + {\it \epsilon}_{ict}$$

Equation 5 estimates the association between loss of power and platform ideologies, conditioned on a moderator variable M _it. Here, the estimators β₁ and β₃ provide estimates of this conditional association. We consider several moderators including the size of the party's leadership selectorate and the past platform shift (a lagged dependent variable).

(5)$$\eqalign{Y_{ict} & = \beta_1\ \rm{Loss \, of \, Power}_{it} + \beta_2 M_{it} + \beta_3\ \rm{Loss \, of \, Power}_{it} M_{it}\cr & \quad + {\boldsymbol \psi}{\bf X}_{ict} + {\boldsymbol \gamma}_t + {\boldsymbol \kappa}_i + \epsilon_{ict}}$$

Our sample consists of all parties and elections for whom MARPOR has coded platforms within relevant OECD countries. As such, the principal comparison is between just-defeated parties and all other parties. In employing this panel data, we make an assumption, consistent with a broad empirical literature on platform positioning, that the right-left scaling of platforms is time-invariant. We partially address concerns about this measurement assumption by replicating our findings on the Lowe et al. (Reference Lowe, Benoit, Mikhaylov and Laver2011) logit-transformed measure of right-left ideology in Figures A9 and A13. This analysis also requires an assumption of time-invariance, but on a different measure.Footnote ⁸

Given concerns about the mapping of electoral outcomes onto loss of power across varying electoral systems, we examine the robustness of our results in both two- and multi-party systems. For all outcomes, we provide analogous specifications that disaggregate two- and multi-party systems, based on the effective number of parties by country (Appendix A6). In multi-party systems, basic theoretical results in the spatial positioning literature do not (necessarily) predict Downsian convergence to the center. In these empirical specifications, we seek to examine whether observed patterns are consistent across both types of party system. In the case of all findings, we cannot reject the null hypothesis that observed associations between loss of power and platform re-positioning are equivalent in two- and multi-party systems.

The model of platform positioning in Section 4 implies that loss of power is endogenous to platform choices. The estimators in Equations 4 and 5 are generalized difference-in-difference estimators when party (i) and election (t) fixed effects are included in the specifications. Because we study a dynamic process, interpreting estimates from these difference-in-difference estimators as (unbiased) estimates of the Average Treatment Effect on the Treated (ATT) is not straightforward. Since a “Loss of Power” can occur in any number of preceding elections, we do not expect the parallel trends assumption to hold in the dynamic process we study. This assumption is standard in motivating identification of the ATT with a difference-in-differences estimator (Angrist and Pishke, Reference Angrist and Pishke2009). As such, we do not interpret our estimates as causal effects. Instead, we examine the stability of our coefficient estimates in a large number of specifications consisting of different permutations of covariates and fixed effects. We report these findings in the form of coefficient stability plots in Appendix A9.

The use of election (contest) fixed effects further allows us to examine within-election variation in platform positioning (i.e., relative to other parties). We look at other specifications to account for competitors’ platform re-positioning in Figures A10 and A14, finding substantively similar results to the fixed-effects strategy described in the main text.

3.1 Centrist platforms

We begin by examining the empirical relationship between an electoral defeat and the party's subsequent ideological positioning. Specifically, we estimate the probability that a party runs on a centrist platform in a given election, controlling for its ideological positioning in the previous election. As described above, we classify a party's positioning by its distance (in country-specific standard deviations) from the mean platform of parties in the country.

Table 1 presents the relationship between loss of power and adoption of a subsequent center platform, showing that electoral defeat in the previous election is negatively associated with the probability of a subsequent run as a centrist party. Adding fixed effects to a base set of controls, we then estimate models with: election fixed effects; party fixed effects; party and decade fixed effects; and party and election fixed effects in columns 2–5. The coefficient of the electoral defeat variable remains negative and statistically significant. In these specifications, the association is significant at the p < 0.005 level. The estimates are sizable: we find that electoral defeat is associated with a 13.7 percentage point drop in the probability of subsequently running as centrist (column 5). Given a baseline probability of 38.9 percent of a party running as centrist, this drop amounts to a 35.2 percent change.

Table 1.

The association between loss of power and adoption of a center platform in election t + 1

Standard errors clustered by party. Note: *p < 0.1; **p < 0.05; ***p < 0.01.

Note that this shift away from the center is the opposite of the predictions of several “decision rules” proposed in earlier studies, which suggested that vote-seeking parties would tend to move to the center, particularly when public opinion moves against them (Adams et al., Reference Adams, Clark, Ezrow and Glasgow2004; Adams and Somer-Topcu, Reference Adams and Somer-Topcu2009).

Figure 1 depicts the distribution of platforms in election t + 1 as a function of electoral fortunes in election t, among parties in government entering election t.Footnote ⁹ The distribution of left, center, and right platforms is similar among parties about to lose versus retain power. While the distribution of platforms remains very similar in election t + 1 for parties that remain in power, parties that lose power in election t tend to adopt non-centrist (left or right) platforms in the subsequent election. In sum, a strong shift away from the center in election t + 1 is apparent only subsequent to a loss of power (center panel).

Figure 1.

This graph depicts the distribution of platforms in the current election (t) and the next election (t + 1) among parties governing parties prior to election t, as a function of the results of election t. We do not detect differences in the distribution of left, center, and right platforms in election t. However, after a loss of power, parties are less likely to adopt centrist platforms (center panel). 90 percent and 95 percent confidence intervals (thick and thin lines, respectively) are constructed from standard errors clustered by party.

We test the sensitivity of the findings to our specification of left, right, and center platforms in Appendix A5. The results remain substantively similar in the neighborhood of our definition, strengthening our confidence in the observed finding that parties that suffered a loss of power are subsequently less likely to run on centrist platforms.

3.2 Shifts to the extreme

Having established the general association of defeat with a lower likelihood of a subsequent run as a centrist in Table 1, we now provide a more nuanced account of changes in party positioning subsequent to a loss of power. First, we consider the direction of ideological shifts preceding elections t and t + 1. The outcome variable is the magnitude of a shift toward the ideological extreme (i.e., away from the center). The advantage of using this outcome is that it applies to all parties; recall, a shift to the extreme is with respect to the party's overall ideological positioning.

Table 2 presents the relationship between the party's ideological shift before the previous election and the subsequent ideological shift after the electoral defeat. Column 1 shows that defeat in itself is not significantly associated with a move to the extreme, but that a shift in the previous elections to the extreme is strongly and negatively associated with the subsequent shift. Put simply, parties tend to “correct” their previous shift by making a move in the opposite direction than the one they had made before the last election. This result is consistent with the argument advanced by Budge et al. (Reference Budge, Ezrow and McDonald2010), but the finding is also consistent with a simple reversion to the mean. Yet as the interaction term in column 2 indicates, electoral defeat is associated with a stronger “correction.” Substantively, the magnitude of this correction is 52 percent larger following loss of power. In other words, parties that suffer an electoral defeat tend to reposition ideologically in the direction opposite to the one they had previously shifted toward, and do so to a substantially larger degree than parties that did not suffer loss of power. This pattern remains consistent as we include fixed effects for election, party, or decade (or combinations thereof).

Table 2.

The association between loss of power and platform shifts toward the extreme, conditional on the previous platform shift

Standard errors clustered by party. Note: *p < 0.1; **p < 0.05; ***p < 0.01.

3.3 The role of the selectorate

In Table 3, we assess the role of the institutional design of the party's selectorate in conditioning electoral responses to loss. In the top panel, we examine the association between the size of the party leadership's selectorate and the direction of the party's ideological shift: Do parties with large selectorates, e.g., ones with open primaries, have a greater tendency to move centripetally toward the median voter? As the top panel indicates, we find no clear association between selectorate size and the direction of the subsequent ideological shift. The interaction between electoral defeat and selectorate size is quite small and far from statistical significance in all specifications.

Table 3.

The association between loss of power and platform shifts, to extreme (top panel) and size of shift (bottom panel), conditional on selectorate size

Standard errors clustered by party. Note: *p < 0.1; **p < 0.05; ***p < 0.01.

In the bottom panel, we examine the size of the ideological shift. Here, our focus is not the direction of the shift—center versus extreme—but rather the magnitude of the change. Using this new dependent variable, the results are quite different. We find that the magnitude of the ideological shift after electoral defeat appears to be conditioned by the size of the leadership selectorate. Examining the coefficients on “Loss of Power_t,” we see a positive and statistically significant relationship between electoral loss and the platform shift prior to the next election. This result is consistent with an earlier finding that loss of vote share is associated with a larger ideological shift in the next elections (Somer-Topcu, Reference Somer-Topcu2009). We also find that the interaction term of loss and selectorate size is negative. When adding party-election fixed effects to improve precision, the point estimate on the interaction term is substantively quite large and negatively signed.Footnote ¹⁰ Substantively, this analysis suggests that parties with a concentrated leadership selectorate respond to electoral defeat with larger platform shifts on average. However, in settings where the leadership selectorate is more diffuse, the magnitude of the platform shift following loss is, on average, not distinguishable from that of parties that do not lose office.Footnote ¹¹

3.4 Post-loss strategies and return to government

Finally, in Table 4, we explore whether the choice of strategy post defeat is associated with the party's subsequent electoral fortunes. In columns 1–3, we estimate the relationship between the direction of the ideological shift and the likelihood of the party returning to power after the next election. As the table indicates, parties that shift to the extreme following a defeat are slightly more likely to be in government after the next election. In substantive terms, for a mean-sized shift to the extreme (13 points on the RILE measure), the chances of returning to power increase by approximately 4.6 percentage points (column 3). In contrast, columns 4–6 show no evidence that the magnitude of the ideological shift post-defeat is associated with the party's chances of returning to power in the next election.

Table 4.

The association between loss of power in election t and return to power in election t + 1, conditional on changes in platform in between the two elections

“To Extreme_t+1” and “Shift Magnitude_t+1” are divided by 100 to scale coefficient estimates. Standard errors clustered by party. Note: *p < 0.1; **p < 0.05; ***p < 0.01.

We graph the results in Figure 2, indicating that a shift to the extreme between elections t and t + 1 benefits the electoral prospects of parties that had just lost power. The left panel in Figure 2 depicts this positive association for parties that lost power in election t (blue) relative to all other parties in the sample (green). It is also useful to condition the sample to parties in power preceding election t (right panel).Footnote ¹² In this graph, shifts to the extreme among re-elected parties are associated with lower prospects of another re-election in contrast to the apparent benefits of moving to the extreme for just-defeated parties.

Figure 2.

Probability of being in power in time t + 2 as a function of electoral outcomes at t and the subsequent shift in platforms in t + 1 (x-axis). The left panel includes all parties in the dataset while the right panel conditions the sample on parties in power at time t. 95 percent confidence intervals constructed upon standard errors clustered at the party level.

Collectively, these findings prove quite robust to modeling choices. In Appendix A9, we examine the robustness of the specifications in Tables 1–4 to alternate weighting schemes, all permutations of covariate and fixed-effect specifications, and alternate operationalizations of our outcome variables. We also examine the possibility that results may differ when one considers loss of power only in instances where the ousted governing party actually experienced a drop in vote share in Appendix A10. In doing so, we address the concern that in parliamentary systems, a governing party may perform as well as in previous elections, or even better, but nonetheless find itself out of power due to the politics of coalition formation.Footnote ¹³ We find no evidence of heterogeneity, thereby strengthening confidence in our interpretation of the findings.

4.1 Setup

There are two parties, labeled L and R, each of which is composed of two factions, one ideologically moderate (denoted M) and the other ideologically extreme (denoted E). In each period, each faction produces one candidate. All candidates from a given faction are ex ante identical, and candidates can run for office only once. In each election at most one candidate from each party may enjoy a quality advantage worth b > 0 to all voters if that candidate is elected. Within a party, this advantage goes to each faction with probability ρ < 1/2, and to no faction with probability 1 − 2ρ. The draws of candidate quality are independent across parties. We denote by b _i ∈ {0, b} the quality level of party i's general election candidate.

Upon election, a candidate from faction j in party i implements her ideal policy $y_i^j \in {\opf R}$.Footnote ¹⁴ The factional ideal points are related to one another as follows:

$$\eqalign{y_R^M & = -y_L^M \quad ( y_L^M < 0) \cr y_R^E & = y_R^M + \delta \cr y_L^E & = y_L^M - \delta}$$

Thus, the parameter δ ∈ (0, b) measures the parties’ internal ideological heterogeneity. Let $\Delta = y_R^M - y_L^M$ denote the distance between the moderate factions; this serves as a measure of partisan polarization. We denote by p _i the ideal point of the party i nominee.

There is a continuum of voters who care about policy and quality. Voters are ideologically heterogeneous, with an electorate-wide ideological median $y_m \in ( y_L^M,\; y_R^M)$. Each party i is associated with a continuum of allied voters with ideal points ${\cal P}_i \equiv [ \underline y_i,\; \overline y_i]$ who form a subset of the general election electorate. This group might represent the set of party i primary election voters. The median of ${\cal P}_i$ is ideologically located midway between the factions, and thus has ideal point $y_i^d = ( y_i^M + y_i^E) /2$.Footnote ¹⁵ Additionally there are two subgroups within ${\cal P}_i$ that support the party factions. For each faction j, ${\cal P}_i^j \subset {\cal P}_i$ represents the set of closely aligned party voters. All members of subgroups ${\cal P}_i^E$ and ${\cal P}_i^M$ are more extreme and moderate than the party median voter, respectively, and the party median belongs to neither subgroup. The median of ${\cal P}_i^j$ has the same ideal point $y_i^j$ as the faction's candidate. The subgroup members receive utility w > 0 when their candidate is elected. This might correspond to faction-specific rents or private goods that a candidate can provide to loyalists.

In each party, candidate selection depends on its current “lead” faction, candidate quality, and the party's selectorate. The lead faction is simply the faction of the previous period's election candidate; that is, nomination determines formal control of the party. At the beginning of the game, the lead faction is M in both parties, which maximizes their electoral competitiveness. Larger selectorates reduce the lead faction's control. Let π ∈ (0, 1) be a measure of the size of party selectorate, and let λ ∈ [0, 1] be a measure of the ease of party leadership transitions following a win. If party i won the preceding election, then with probability πλ, the set of all party voters ${\cal P}_i$ chooses the party's candidate, and with probability 1 − πλ, the lead faction's voters choose. We refer to the former as an open process, and the latter as a closed process. Likewise, if party i lost the preceding election, the process is open with probability π and closed otherwise. Thus, the party members are better able to choose leaders elites following losses, regardless of whether the party held power preceding the loss.

The nominated candidates finally compete in a general election by offering their ideal policies as the party platforms. Voters choose on the basis of policy utility, candidate quality, and a random utility shock ω ~ U[ − α, α] in favor of party R. The median voter receives higher stage game utility from party R if:

(6)$$ - \! \vert y_m - p_R \vert + b_R + \omega > -\vert y_m - p_L \vert + b_L .$$

We make two assumptions to eliminate a few uninteresting cases. First, to avoid corner probabilities of victory, we let α > Δ + δ + b. Second, to assure that faction members care enough about their own candidate's selection to act differently from their party's median voter, we assume that w satisfies:

(7)$$w > \max \left\{{( b + \delta) ^2 + \alpha ( b - \delta) + 2 b \Delta\over \alpha - \Delta - \delta - b},\; {\left(\alpha + \Delta + 2 b - \delta \right)( b - \delta) \over \alpha - \Delta - b} \right\}.$$

Figure 3 illustrates the configuration of voters in one party. The sequence of each period of the basic game is as follows.

1. 1. Nature reveals the quality level of each faction's candidate in each party to all players.

2. 2. In each party, Nature simultaneously chooses whether the nomination process is open or closed.

3. 3. In each party, the nominating players vote to nominate a candidate.

4. 4. Nature draws ω.

5. 5. All voters vote to determine the election winner.

Figure 3.

Party R Voters. All party R voters have ideal points in the interval $[ \underline y_R,\; \overline y_R]$. In an open process the party median voter with ideal point $y_R^d$ is decisive in selecting a candidate. In a closed process, the factions, with decisive voters at $y_R^M$ or $y_R^E$, will be decisive.

There are many equilibria in this game, and we therefore use the fact that voters cannot be pivotal and are effectively indifferent among voting strategies. We focus on the subgame perfect equilibrium where each voter acts as if pivotal and chooses the candidate who maximizes expected utility in the upcoming general election. In the candidate selection stage, each eligible voter's nomination strategy maps the previous history of elections and quality revelations to a vote between factions. In the general election, voter strategies map election history, current quality and candidate realizations, and the electoral shock to votes between the L and R candidates. Thus, voters do not necessarily choose the closest candidate at the nomination stage, but disregard the effect of their votes on lead factions in future periods.

4.2 Equilibrium

We begin with an analysis of the stage game. Since candidates live for only a single period and voters are never pivotal, the only way in which actions in one period affect another is through the identity of the parties’ lead factions and the current incumbent party (i.e., the winner of the preceding period's election). The stage game equilibrium can therefore serve as the basis for analyzing the infinite horizon game.

As the median voter is pivotal in the general election, we begin with her decision. After the shock ω is realized, she simply chooses the optimal candidate according to Equation 6. This implies the following probability of victory for party R:

(8)$$\phi( p_L,\; b_L,\; p_R,\; b_R;\; y_m) = {1\over 2} + {2 y_m - p_R - p_L + b_R - b_L\over 2 \alpha} .$$

Now consider party nominations. As in the general election, the median voter in the candidate selection process is decisive. There are two cases. First, when the nomination process is open, the party median (with ideal point at $y_i^d$) will prefer the high-quality candidate, if one exists. The most interesting subcase is the one in which the extreme candidate is high quality. The voter is indifferent between factions on ideological grounds, but receives higher utility from a high-quality faction E candidate. Since b > δ, an extreme high-quality candidate will also be more appealing than a low-quality moderate in the general election. In every other subcase, the moderate is more electable and thus receives the nomination.

In the second case, the process is closed and the nominating body is the lead faction's allies. These voters obviously prefer their own faction on ideological grounds, but may sacrifice quality and electability (for faction E voters) by choosing their own candidate. By assumption 7, factional voters intrinsically benefit from nominating their own candidates. This induces them to prefer their own faction's candidate despite inferior quality.Footnote ¹⁶

We summarize these cases in the following result. A proof is provided in Appendix A13.1.

The stage game therefore captures a simple source of variation in policy platforms. Platforms reflect candidate quality when the candidate selection process is open (e.g., in a primary election), and reflect the party leadership's preferences when the process is closed. Candidate selection processes are therefore an important driver of the distribution of platforms over time.

The persistence of the lead faction across periods drives the platform dynamics of interest. To illustrate, consider what happens if, under the open procedure, a party nominated its extreme faction (E) in period 1 because of its high valence. This candidate is relatively likely to lose, but regardless of the result faction E remains the period 2 lead faction and automatically nominates its own candidate under a closed procedure. By contrast, a high valence M candidate in period 1 is relatively likely both to win and to nominate a moderate in period 2. These extreme cases play a significant role in the probabilities of extremism following a loss and moderation following a win.Footnote ¹⁷

Our next three results show that under some modest assumptions, the model makes predictions that are consistent with the main empirical results on platform positioning (we leave results on returning to power for future work). All assume that the median voter is unbiased ideologically, which ensures that parties are equally likely to win the first election and that subsequent platform moves are not due to an ex ante partisan advantage. Proofs are provided in Appendix A13.3.

Table 1 shows that an electoral defeat reduces the subsequent probability of a centrist platform. Remark 1 correspondingly shows that if intra-party ideological heterogeneity is sufficiently high, the event of losing in one period and running as an extremist in the next is more likely than that of winning and running as an extremist.

The result is driven by the fact that a party is more likely to lose when its selectorate opts for its extreme faction. This does not imply that party members err in choosing the extreme faction under an open procedure, as choosing a low-quality moderate would be even worse for the party. Along with the persistence of lead faction status over time (due to the possibility of a closed procedure), the correlation between an extreme candidate and losing in period 1 generates a correlation between losses and subsequent extremism.

Remarks 2 and 3 provide analogous findings for the likelihood of platform adjustments. The former addresses the relative probabilities of reversing a preceding platform shift—i.e., changing to an extreme platform in period 1 and reverting back to moderation in period 2—following a loss versus following a win, as reported in Table 2. The latter addresses the probability of any platform shift between periods, as reported in Table 3.

Reversing or adjusting a platform is more likely following a loss with an extremist candidate, since extreme platforms are more likely to be abandoned than moderate platforms when candidate selection is open. As in Remark 1, the correlation between an extreme candidate and losing in period 1 then implies that events that are more likely under an extreme lead faction will also be relatively more likely following losses.

The overall implication of these remarks is that sequences of losses followed by the events of choosing an extreme platform, reversing a platform shift, and making a platform shift should be observed with greater frequency than the respective sequences starting with wins. Importantly, since each party wins the election with equal probability under an unbiased median voter, the remarks further imply that the conditional probabilities of these events following losses are higher than those following wins.

The comparative statics on selectorate size following loss versus victory are more ambiguous. Differentiating the difference in the likelihood of adjusting platforms after a loss versus after re-election with respect to π shows that the relationship can be increasing or decreasing. For some regions of the parameter space, this difference is decreasing in selectorate size, consistent with the finding in Table 3. However, this relationship does not generally hold across the entire parameter space.

4.3 An infinite horizon model

Extending the model to an infinite horizon allows us to examine the long-run evolution of party platforms. This is valuable because we can account for the relative frequency of starting conditions for incumbents lead factions, as well as examine comparative statics over a large subset of the parameter space.Footnote ¹⁸ Formally, we model the equilibrium of the game as a Markov process, taking lead factions and previous winning party as a state variable, and apply standard techniques to analyze long-run behavior. Appendix A13.2 provides the details of this model.

Unfortunately, calculating the equilibrium of this game requires numerical simulation because of the complexity of many of the equilibrium expressions. This subsection illustrates comparative statics for each of the quantities of interest addressed by Remarks 1–3. The reported probabilities are for party R; note that all results are symmetric for party L given the symmetry in factional ideal points.

We first examine the probability of running on an extreme platform. Recall our main empirical finding from Table 1 that subsequent to electoral loss, former governing parties are less likely to run on centrist platforms. We examine this relationship in the theoretical model by differencing the probability of running on an extreme platform after losing power versus winning re-election. Figure 4 provides comparative statics on this difference across a range of y _m (ideological bias in the electorate) and π (selectorate sizes). Consistent with the empirical results, even absent bias in the electorate or restrictions on the incumbent (i.e., y _m = 0 and λ < 1), this difference is positive. Party R is increasingly likely to resort to extreme platforms following losses versus wins when the party is electorally disadvantaged (y _m < 0). Moreover, party R is more likely to lose when y _m < 0, which may help to account for observed patterns in the data.

Figure 4.

Difference in probability of running on an extreme platform after a loss of power versus winning re-election for the right party. In this graph, α = 2.5, b = 0.65, $y_R^M = 0.3$, δ = 0.5, and ρ = 0.25.

Several additional comparative statics on the difference in probability of running on an extreme platform yield additional insights. Restrictions on the incumbent's ability to change platforms (λ) result in larger differences between winning and losing parties’ adoption or maintenance of extreme platforms. Perhaps less obviously, this difference is increasing in both polarization (Δ) and intraparty ideological heterogeneity (δ).

Our empirical results in Table 2 suggest that electoral defeats generate larger reversals of the preceding platform shifts. In the context of Remark 2, such a reversal indicates either a change in one party from moderate to extreme in election t and then back to moderate in election t + 1, or a shift from extreme to moderate and back to extreme. We estimate the probability of observing either pattern when an incumbent party loses in election t versus wins re-election in election t. This difference in probability of ideological reversal for the right party is plotted in Figure 5. We note that with no ideological bias (y _m = 0) and no additional friction on the incumbent party's selection process (λ = 1), this difference is positive (if small). It increases in magnitude in the region in which the right party is disadvantaged (y _m < 0) and loss is consequently more likely. Similarly, it increases in magnitude when additional constraints are imposed on the incumbent's ability to open leadership selection (λ < 1). Furthermore, this difference is increasing in both polarization (Δ) and intraparty ideological heterogeneity (δ). In sum, under “neutral” conditions as well as electoral conditions more conducive to loss, the probability of ideological reversal in consecutive periods is higher following electoral defeat than after re-election.

Figure 5.

Difference in probability of ideological reversal after a loss of power versus winning re-election for the right party. In this graph, α = 2.5, b = 0.65, $y_R^M = 0.3$, δ = 0.5, and ρ = 0.25.

Finally, we turn to the finding that ideological repositioning is mediated by the size of the selectorate, described in Table 3. The interaction model implies the need to investigate two theoretical quantities of interest. First, we assess the “main effect” that the magnitude of electoral repositioning is greater following a loss than a victory. Theoretically, this corresponds to the probability of shifting from the moderate faction to the extreme faction or vice versa. Figure 6 reveals that indeed, under symmetric, neutral conditions (y _m = 0 and λ = 1), losing parties are slightly more likely to reposition than winning parties, given the positive estimates of the difference. The magnitude of this difference is increasing in electoral disadvantage (y _m < 0) and selection constraints on the winning party (λ < 1).

Figure 6.

Difference in probability of platform adjustment after a loss of power versus winning re-election for the right party. In this graph, α = 2.5, b = 0.65, $y_R^M = 0.3$, δ = 0.5, and ρ = 0.25.

The negative coefficient on the “conditional effect” from the interaction models implies that this difference should be decreasing in selectorate size (π). Figure 6 further depicts the numerical results on this difference with respect to selectorate size. As in the analytical results, the comparative statics with respect to π are more ambiguous, revealing a sometimes increasing relationship between selectorate size and the difference in platform adjustment between losing and winning parties (see right panel of Figure 6).