1 Introduction. Retrieved Labour obtained 27.6% of the vote in the 1983 election, down 9 points from their 1980 defeat.

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1 Tactical Extremism Jon X. Eguia Department of Economics, Michigan State University and Department of Economics, University of Bristol Francesco Giovannoni Department of Economics, University of Bristol Abstract We provide an instrumental, rational choice theory of extreme campaign platforms. By adopting an extreme platform, a party foregoes some probability of winning the current election. However, the party also builds credibility as the one most capable of delivering an alternative poliy. If voters become disatisfied with the status quo, they will then turn to the party that had adopted an extreme policy and kept it in opposition.

2 Introduction Political parties occasionally choose extreme candidates who seem destined to lose. In the US, following their defeat in the 960 Presidential election, the Republican party chose the extreme right-winger Barry Goldwater as their 964 candidate. Goldwater lost in a landslide election. In the UK, following their defeat in the 979 General election, the Labour party veered left under Michael Foot. Their socialist manifesto for the 983 election under Michael Foot was famously described as the longest suicide note in history. In the 983 election, Foot led Labour to their worst electoral result since 98. In 05, following their second consecutive election defeat, Labour again selected a candidate from the far left: Jeremy Corbyn. Traditional spatial explanations Downs 959 suggest that parties should follow the median. If a leftright-leaning party loses, under traditional models of two-party competition, one infers that the party was located too far to the leftright for the median s taste, and one predicts that in the next election the party will correct this mistake by moderating positions, selecting policies closer to the center. One may wonder why the Republicans in 964, or Labour in and 05, responded to defeat by doubled down and becoming more extreme. Non-instrumental theories would account these choices as expressive see for instance Brennan and Hamlin 998. Purist partisan factions Roemer 009, ch. 8 have preferences that depend on the platform embraced by their party, and not by the political outcome. Extreme policy platforms are more satisfying to these factions, even if they spell electoral doom. We suggest an alternative, purely instrumental, explanation with testable empirical implications. We argue that even offi ce-motivated parties that care only about winning elections, under some circumstances, have incentives to choose an extreme policy that makes them lose the most immediate election. The reason is that there are more elections after the most immediate one. Choosing an extreme policy is akin to leaving the ground fallow for a year: in the short term it leads to a loss, but in the long term it makes the ground more fertile and increases future yields. We argue that choosing an extreme policy has a similar effect. It allows the party to gain competence in such an alternative policy, and in expectation it delivers better electoral results in subsequent elections. Parties can have different skills at implementing particular policies Krasa and Polborn 00, 0, 06. Put differently, party valence can be policy specific. Suppose that an incumbent party has gained greater policy-valence at the status quo policy favored by the median voter. We can say that this incumbent party owns the issue Petrocik 996. Now consider the options available to the opposition party. It could try to compete on the same issue by selecting the same status quo policy. But given that the incumbent has a policy-valence advantage on this policy, the party is not likely to win. Alternatively, the opposition party can go an explore an alternative policy, which we label extreme simply because it is outside the mainstream. This extreme policy is less liked by voters, so choosing it reduces the probability that the opposition party wins the election. To convey the argument in its most stark case, assume that choosing the extreme policy makes the opposition lose the election with certainty. By choosing a new alternative policy position, the opposition party invests time and resources into developing and perfecting proposals on this policy position. These position-specific investments make the opposition party more competent on this alternative position. It is then able to produce higher quality proposals. As in Hirsch and Shotts 005, let a proposal be defined by two quantities: its ideological position as in traditional spatial models and its quality. Quality is a valence characteristic that all voters appreciate. By repeatedly investing on a particular policy position, a party gains the ability to generate proposals of higher quality on this position. It may also allow the party, if it perseveres in choosing the alternative policy after the electoral defeat, to gain credibility as the party that will deliver this alternative. An opposition party that embraces an alternative position will eventually own this position if it perseveres in holding it. It will have the policy-specific advantage in this alternative policy position. Suppose that the implemented policy is the mainstream one and the country suffers a negative shock. Perhaps the economy does not perform as well as expected. If the median voter becomes disillusioned with the status quo policy, Goldwater DW-Nominate score of 0.67 locates him among the 3% most conservative senators in the history of the US Senate see Carroll, Lewis, Lo, McCarty, Poole and Rosenthal on voteview.com, updated September 05. He lost 6% to 38%. The quote is by Labour MP Kauffman. See Mann, Nyta Foot s message of hope to left. BBC News. Retrieved Labour obtained 7.6% of the vote in the 983 election, down 9 points from their 980 defeat.

3 she might conclude that it is not the right policy, and that a new one is needed. And the opposition party will have an alternative ready, one in which it has invested over time so it built a policy-specific valence advantage. Therefore, extremism can help to win future elections by positioning the party as the party that is most capable of delivering a high quality alternative policy. The party surrenders competition over who can best provide policy x today, by investing in policy y, becoming the best at policy y, and hoping that voters will want y at a future election. We expect a party to choose this tactical extremism under the following circumstances: -the party is currently out of power, and it is regarded as less competent or less trustworthy or both in delivering policies at the currently mainstream position. -the consensus in favor of the currently preferred, mainstream policy position is weaker. Returning to our examples, the Republicans in 964 and Labor in 983 were out of power and faced popular opponents such as Johnson and Thatcher. If they perceived their chances of victory competing at the center to be small, then they had greater incentives to try an alternative. Labour chose the left-leaning Michael Foot in 980, at the tail-end of the stagflation crises of the 970s. GDP growth per capita was lower in the years preceding the election of Foot than at any other time from the Great Depression in the 930s to the Great Recession in We conjecture that Labour hoped that further crises would make voters turn away from capitalism and seek an alternative in the 983 election. By choosing Foot, Labour would have been ready to deliver such an alternative. Tactical extremism sometimes pays off, other times it does not. Barry Goldwater s defeat set the stage for the rise of conservatism Perlstein 009 and was followed by a sequence of conservative victories in several states, capped with the ascension of another conservative Reagan to the presidency in 980. On the other hand, Foot s extremism flopped: the British economy rebounded in the early 980s, the UK won the Falklands Malvinas War and Thatcher became more popular. Labour backtracked, ditching its investment in socialism as a sunk cost, and returning to compete and to lose throughout the 980s on centrist ground. Extremism is the best course of action for a party only in rare circumstances, so we expect tactical extremism to be observed only rarely. It is more likely to emerge in periods of greater upheaval, in which the previously mainstream orthodox policies have been called into question, such as following the 99 Depression, leading to tactical extremism in the 930s; following the 970s stagflation, and following the Great Recession. These or future shocks to the orthodoxy can make a policy experiment more appealing for parties with low-valence at the currently orthodox policy. These parties will be tempted to embrace an alternative and invest in it, hoping that additional negative shocks further sink the popularity of the orthodox policy and that voters follow the party to the policy alternative. Our theory formalizes these intuitions. The rest of the paper is structured as follows. In Section we introduce a simple model which we analyze in Section 3. We discuss and interpret our results in a concluding Section 4. We relegate most of our proofs to an Appendix. The Model Consider a two-period model of electoral competition with two purely offi ce-motivated parties and one strategic representative voter. In each of the two periods, parties E and M compete for election. Both parties seek to maximize the sum of the probabilities of being elected over the two periods. We consider a policy space with only two policies: {, }, where represents the orthodox or mainstream policy, and an alternative or unorthodox policy that we call extreme. In each period t {, }, before the election, the two parties simultaneously choose a policy. We denote with x j t {, } the policy choice of party j {E, M} in period t, while x t = x E t, x M t denotes the policy profile chosen by the two parties in period t. Once a policy profile is chosen, the voter chooses one of the 3 Inflation-adjusted GDP growth per capita in the UK from 973 to 980 was less than %. Since 945, the only other span of more than four years of such low growth occured from 007 to 04..., and once again Labour has chosen a candidate from its extreme left. Source of the data: UK Offi ce of National Statistics, GDP average per head, Chained Volume Measures CVM market prices

4 two parties. The winning party implements her chosen platform as period t. Let x W t { } x E t, x M t denote the policy of the winning party. The voter cares about the state of the economy. Assuming that there is an underlying state of nature θ {, } that determines which policy delivers a better economic outcome. In each period t, the economy performs better if x W t = θ than if x W t = θ. The true realization of θ is never observed by any of the players, but in period t = it is common knowledge that Pr θ = = p >. We therefore refer to platform as the mainstream platform and as the extreme platform because ex-ante policy is most likely to be the policy that generates a better economic outcome. Since θ {, }, we refer to policy θ as the correct policy and θ as the wrong one. The economy is also subject to temporary external shocks in each period, which are independent of policies. Let ω t {, } denote the period t external shock. We assume that true realizations of ω and ω are never observed by any of the players, but it is common knowledge that these two random variables are independent across the two periods and identically distributed with Pr ω t = = q >, so we interpret ω t = as a normal state, and ω t = as a negative shock. A third component that affects the performance of the economy is the competence of the party in government at executing its policy. Whether an implemented policy is the right one x W t = θ or the wrong one x W t = θ given the state, if it is implemented competently, the economic output is increased by c 0,. We assume that party M, the mainstream party, starts the game with greater competence at the mainstream policy, and it owns the issue, in the sense that it maintains a valence advantage on this policy position as long as it continues to advocate for it. Formally, for each party j {E, M}, let c j xj denote the competence or valence advantage of party j in period over policy x j, and let cj xj, xj denote the period competence of party j on policy x j, given xj. We assume that cm = c, c M, = c and c M, = 0, whereas c E = c E, = c E, = 0. On the other hand, the extreme policy position is open territory, up for grabs in the sense that it is not owned by any party. A party that invests on it for two periods in a row gains greater competence on it. Formally, c j = cj, = 0 and cj = cj, = c for each j {E, M}. Notice the deliberate asymmetry in the model: the mainstream party M starts the game with a valence advantage over the extremist E over the mainstream policy. Party M owns this policy position. Party E can only acquire a credibility advantage if she consistently pick the extreme policy and M does not imitate her. 4 The economic utility that the voter obtains from electing party j in the first period is: θx j + ω + c j xj and the economic utility that the voter obtains from electing party h in the second period is, θx h + ω + c h x h, x h. In addition, we assume that a random variable ɛ t represents the voter s idiosyncratic preference for party M, as a stochastic party valence characteristic in each period. This shock captures non-policy attributes such as charisma or attractiveness of the candidate. We assume that ɛ and ɛ are i.i.d. distributed as uniforms on, and private information to the voter, so that they are not observed by the parties. It is convenient to define π t = θx W t + ω t. The voter s utility from choosing party j in the first period is vθ, w, x j = π + c j xj + I j=mε, where I j=m is an indicator function equal to one if j = M and zero if j = E. The voter s utility from choosing party j in the second period is vθ, w, x j, xj = π + c j xj, xj + I j=mε. 4 The fact that we allow the possibility that M can match E s credibility over the extremist platform is simply there to make it harder, in principle, for E to choose the extremist policy over a version of the assumption where M cannot do that. Choosing the latter version of our assumption would obviously make our results no easier to obtain. It actually turns out that in equilibrium M will never choose policy - in the first period and so either version leads to the same results. 4

5 We assume that in each period, the voter maximizes her period s utility, voting for the candidate that delivers a higher expected utility in this period. We also assume that in each period, after the winning party is determined and her platform implemented, π t is commonly observed by all players. 3 Analysis In this section, we describe equilibrium behavior. We relegate all formal statements and their proofs to the appendix. Throughout, we assume that in either period, if M is indifferent between two platforms, she chooses the mainstream one. We begin with the second period. We determine updated beliefs about the true state θ given the events of the first period. If the first period economic outcome is one that could only have been achieved by the correct policy if π = or only by the wrong one if π = platform, then the correct policy becomes known: if π =, θ = x W, whereas if π =, then θ = x W Lemma. If the correct policy becomes known, both parties propose it in the second period. Intermediate economic outcomes π = 0 lead to continuing uncertainty about which policy is correct. If the updated beliefs that the correct policy is the mainstream one are suffi ciently high or suffi ciently low, then both parties will choose accordingly, but because the asymmetry in credibility we have introduced in the model, it also also possible that when these beliefs are not so clear-cut, then one party will choose the mainstream policy and the other the extremist one. Because M has an advantage on the mainstream policy, if the parties do choose different policy, it must be party M that chooses the mainstream policy and party E that chooses the extremist one Lemma. So, in summary Remark Policy choices in the second period. If the outcome from the first period generates beliefs such that it is unlikely or impossible that the mainstream policy is the correct one, then this will lead both parties to choose the extremist policy, while if the beliefs imply that the mainstream policy is likely or certain to be the correct one, then both parties will choose the mainstream policy. For intermediate beliefs, the extremist party chooses the extremist policy and the mainstream party choosing the mainstream policy. Given a first period outcome with remaining uncertainty about the correct policy π = 0, the updated beliefs on which policy is correct depend on p prior that the mainstream policy is correct, on q probability of no external negative shock, and on which policy was implemented in the first-period. Lemmas 3-6. In particular, subject to an outcome with lingering uncertainty, If the mainstream policy is implemented in the first period, the beliefs that the correct policy is the mainstream one will be increasing in p and decreasing in q. A mediocre first period outcome means that either the policy choice was wrong or the winning party was unlucky ω =. A higher value of p makes it more likely that the mediocre outcome was due to back luck on the state ω while a higher value of q makes it more likely that the mediocre outcome was due to bad policy. If the extreme policy is implemented in the first period, then the beliefs that the extreme is the correct policy will be increasing in both p and q. Now, it s the extremist policy that has delivered a mediocre outcome and both a higher value of p and a higher value of q make it more likely that the mediocre outcome was due to a bad policy choice. Consider now the first election. The voter votes for M if and only if E[v θ, w, x M ] E[v θ, w, x E ], where E[v] denotes the expectation of v with respect to ω and θ. Detailed results are in Lemma 7, summarized here 5

6 Remark Voter s choice in the first election. If the two parties choose the same policy, then the voter s decision depends only on her idiosyncratic preferences shock and on the policy-specific competence advantage of each party. In particular If both choose the mainstream platform, then M has an advantage and wins with probability + c. If both choose the extremist platform, then neither party has an advantage and M wins with probability. If the two parties choose diff erent platforms, then the voter s decision also depends on the probability p that is the correct policy. In particular If M choose the mainstream platform while E chooses the extremist platform then the probability that M wins is min c + 4p 3 ; If E choose the mainstream platform while M chooses the extremist platform then the probability that M wins is max 5 4p; 0 One simple but crucial observation is that if we consider the first period game in isolation, it is a dominant strategy for E to choose the mainstream policy. Thus the only possible rationale for E choose the extreme platform is to sacrifice some probability of winning in the first period to build a competence advantage on the extremist policy so as to get a higher probability of winning in the second period. Using the same logic, it is also easy to see that M has no incentive to choose the extremist policy Lemma 8. M already enjoys an advantage on the mainstream platform which is also more likely to be the correct one. Choosing the extremist policy in the first period yields no short or long term gain for M. This means that in the first period, only two possible equilibrium profiles may emerge: both parties go mainstream or M goes mainstream while E goes extreme. We describe the conditions under which each of the two possibilities obtain. We focus on the case in which the mainstream policy always wins in the first period election. This makes choosing an extremist policy for E as diffi cult as possible. That is, this is the hardest case for the tactical extremism phenomenon that we want to describe. Remark 3 First period policy proposals Propositions and simplified. Assume p 5 8 c 4. The mainstream policy is implemented in the first period. M always chooses the mainstream policy in the first period while there exist a function ĉp, q and a function q p where and ĉp, q = p q+ if q q p +4p q if q p < q p if q > p q p = 9 p 4p 48p + 08p 48p 3 + 6p p such that E chooses an extremist platform in the first period if and only if c ĉp, q. 5 Further, ĉ is increasing in p and decreasing resp. increasing in q whenever q p < q p resp. otherwise, while q is increasing in p. The portion of space p, q, c above the surface in the figure below is the set of parameter values for which E will select an extremist policy in the first period. Our results partitions the space of possible parameter values in three possible regions. 5 In the appendix, proposition is stated quite differently and in its proof we discuss show how to obtain this simplification. 6

7 Figure : cp,q. In the first region, q is smaller than q p. This means that in the second period, even if the mainstream policy delivered a mediocre outcome in the first period, all players have suffi ciently strong beliefs that the mainstream policy is the correct one that both parties will propose it in the second period. Thus, if the outcome from the mainstream policy is good or mediocre, then going extreme in the first period does not pay off. Only if c is suffi ciently large and p not too large, E is willing to choose the extremist platform gambling that the outcome will be bad. If that happens and it is more likely to happen the lower p is, having invested on the extremist policy from the first period will pay off for E in the second period, when both parties will go extreme.. In the second region, q is larger than p. Now, in the second period, if the mainstream policy delivers a mediocre outcome in the first period, all players blame the policy itself for the outcome, and both parties go extreme in the second period. Thus, going extreme in the first period pays off in the second whenever the first period outcome from the mainstream policy is bad or mediocre. So, again if c is suffi ciently large but not necessarily as large as in the previous case and p small enough but not necessarily as small as in the previous case then investing on the extremist policy is profitable for E. 3. In the third region q is between q p and p. The intuition here is similar to the one in the previous case, except that when the outcome is mediocre, parties will split their proposals, with M choosing the mainstream and E choosing to go extremist. As already discussed above, this will happen because M has an advantage on the mainstream policy that E doesn t have and given that there is suffi cient uncertainty about what is the correct policy, this uncertainty is suffi cient to generate the split. A first period investment on an extreme policy pays off for E if the first period outcome from the mainstream policy is bad or mediocre. So, again if c is suffi ciently large and p small enough then investing on the extremist policy is profitable for E. In all three regions, E makes an extreme proposal in the first period if c is suffi ciently high and p is suffi ciently low, because an increase in c increases the benefits resp. losses from having a competence advantage resp. disadvantage, which pushes E away from the mainstream policy. Whereas, an increase in p makes the mainstream policy more reliable or, equivalently, the extremist one less reliable. How q influences E s choice between mainstream and extremist proposals is more ambiguous. In particular, conditional on q being in the first two regions so that it is suffi ciently large or suffi ciently small, an extremist 7

8 proposal is less likely as q increases, while when q is in the third region then an extremist proposal is more likely as q increases. These can be explained as a combination of two effects. The first effect is the direct effect of an increase in q on first period outcomes. In all regions, an increase in q makes it less likely, from the first period s perspective that an outcome favorable to the extremist choice will occur. For example, if q is suffi ciently small to be in the first region, then a marginal increase will make it a little bit more likely that the outcome is either good or at least mediocre, and in those cases being an extremist in the first period does not pay. 6 If q is in the second or third region, a marginal increase in q will make it a little bit more likely that the outcome is good. 7 The second is the effect of an increase in q on the probability that the pivotal voter in the second period will vote for E. In the first and second region, this effect does not apply because both parties choose the same platform. In the third region, however, M chooses the mainstream policy and E chooses the extremist policy. A marginal increase in q therefore, will change the pivotal voter s beliefs in favor of the extremist policy. Thus our comparative statics results obtain because the second effect is suffi ciently strong in the third region to overcome the first effect. In the other two regions, only the first effect obtains. The figure below plots ĉ p, q for fixed p. E chooses the extremist policy in the first period in the shaded region. The vertical dotted lines represent q p and p respectively. Think of a situation where q is very close to the lower bound / and where E is indifferent between choosing a mainstream or an extremist policy in the first period. In the figure, we are at the point where the horizontal dotted line touches the vertical axis, at ĉ p,. In this situation, since q is very low, all players still believe that a mediocre outcome is not the mainstream platform s fault. Keeping c and p constant at ĉ p, and p respectively, but letting q increase, this remains the case but the probability that a bad outcome occurs also decreases and so E now prefers to choose the mainstream policy. At some point, q is large enough that conditional on a mediocre outcome, E switches to an extremist policy while M keeps choosing the mainstream one in the second period. In the figure, we are crossing the first vertical dashed line which represents q p. As q increases further, beliefs conditional on a mediocre outcome become more and more favorable for the extremist policy and so the incentive to go extremist in the first period as well for E increase until at some point, E decides to do it and enters the shaded region. Eventually, q will be high enough that conditional on a mediocre outcome, M will also switch to the extremist policy in the second period. In the figure, this is the second vertical dashes line which represents p. Now, as q increases, because the two parties are choosing the same platform, all that matters is that an increase in q makes a good outcome more favorable but it s effect conditional on bad or mediocre outcomes does not matter. So, the incentive to choose an extremist policy starts to reduce again. The next figure shows how the three regions change as a function of p: the higher curves represent higher values p and shows how, as p increases the space of values of c, q for which E goes extreme in the first period, becomes smaller. 6 The probability that the outcome is either mediocre or good is p q = p + q p which is increasing in q. 7 The probability that the outcome is good is. Thus, whichever region we are in, the probability of obtaining first period outcomes that favor extremism, is decreasing in q. 8

9 0.5 c q^p q p 9

10 c q 4 Discussion We identify conditions under which an offi ce-motivated political party chooses an extremist policy that causes it to lose an election. Namely, the party must face a disadvantage if it competes on mainstream ideas; the party must be able to acquire a policy-specific valence advantage on an alternative extreme policy; and there must be suffi cient uncertainty in the mind of the electorate about the virtues of the mainstream policy. The idea is that if a party takes an extreme position that is currently unpopular and loses, and the economic outcome under the implemented mainstream policies is bad, voters may then infer that it is time for a new policy. If so, the party that had previously invested in a non-mainstream policy will be better positioned to deliver such an alternative. It follows that extremism is more likely to arise at a time of crisis, when it is more likely that the economic outcome under mainstream policy will be unsatisfactory to voters. Our binary policy space represents a stark contrast between competing policy prescriptions. We see this policy choice as a reduced-form encapsulation of competing political ideologies. Our interpretation of a mainstream policy is the set of economic policies that are applied in most OECD countries, with IMF, World Bank, ECB and Federal Reserve support, centered around a broad consensus that central banks ought to be independent of political control, that private property rights help competitive markets function, that fiscal responsibility is desirable, that free trade generates growth, that inflation targeting should be taken seriously, etc. We think of the parameter p as the probability that such orthodox policies are correct. This underlying value of p may also be different across countries. The whole package of the Washington consensus may not be as appropriate in certain developing countries as it is in others. We interpret p as largely stable over time, but major events can affect it. For instance, the collapse of the Communist bloc in the late 980s would suggest that the capitalist orthodoxy was a better policy prescription. On the other hand, the controversies 0

11 surrounding the policy responses to the Great Recession in the years following 007 show that p is not one, and doubts about the wisdom of austerity, budget balances, and defaulting on the national debt persists. Extremism is more likely to develop when the consensus on the mainstream weakens, so an economic failure is more likely to be blamed on failed policies than on bad luck. Parameter q represents the probability that the non-policy factors that affect the economy are normal. Any possible negative shock that may derail a country s economy regardless of the economic policies implemented in the country would be captured in the probability q. This term includes both country-specific effects, such as the probability of a violent outbreak in unstable countries, or a fall in commodity prices in countries that rely on the export of a given commodity. It also includes the possibility of contagion from a worldwide economic crisis that generates unavoidable negative spillovers due to a contraction of trade, loss of confidence in financial markets, etc. If a negative shock is very unlikely q very high, then the incentives to go extreme increase in the probability of a negative shock decreasing in q because a negative economic outcome would be interpreted as a failure of the mainstream policy. On the other hand, if the negative shock is suffi ciently likely, the comparative static reverses as a disappointing economic outcome would not be blamed on the policy, but on the likely negative shock. We have modelled the incentive for choosing an extreme policy through parameter c, which is the reward for investing on a new policy away from the mainstream. We have interpreted c as an acquired policy-specific valence, obtained as the party becomes more competent on this policy position and is able to generate higher quality policies on this position. Our main intuition is that tactical extremism arises when a party that finds it diffi cult to compete on mainstream policies can adopt an alternative policy in which it gains an advantage, in hopes that a negative economic shock discredits the mainstream policy. This incentive to go extreme is reinforced through other channels that we have not considered. Relax the strong assumption of commitment to any policy proposal. In reality, parties may find it diffi cult to commit to a new policy: reactionary elements within the party will object and fight to row back the changes, so that even if it wins, the party may not implement its policy proposal. If a party has always stood on an ideological position, and it suddenly reverses itself and proposes something entirely different, its proposals may simply not be credible. It may take time to acquire this credibility. In particular, suppose that if a party proposes a new policy, voters treat its platform as stochastic, assigning some weight to its past position in the previous election, and some to the new proposal. If so, a new incentive for tactical extremism arises: a party that proposes an alternative policy position in period and insists on that position in period is more credible in period than a party newly arrived at this position. So a party that is disadvantaged at the mainstream position has an additional incentive to relocate early to an extreme, hoping to become a credible alternative, that voters follow later, after they become disillusioned with the mainstream. The competence and credibility channels reinforce each other: a party chooses tactical extremism, forgoing a small chance to win the current election on mainstream grounds, in order to build an advantage to fight the next election on an alternative policy position. This strategy pays off if the economic outcome in the first period after the mainstream policy is implemented turns out to be negative, thus discrediting the mainstream policy, and inducing voters to seek an alternative. Tactical extremism allows a party to become the new home for these voters, and to win the next election and is more likely to develop when the consensus on the mainstream weakens, so an economic failure is more likely to be blamed on failed policies than on bad luck. [An Alternative Interpretation with naive more gullible voters, that by investing in extreme candidate can change perception of p, would lead to the same thing]. 5 Appendix Some conventions. Let p be the posterior belief, after the economic output π is realized, that the state is θ =. For each candidate J {E, M}, for each second period policy profile x {, } and for each p [0, ], let u V J x E, x M, x E, x M, p be the expected second period utility for the voter from voting for candidate J given x E, x M, and p.

12 Lemma If π =, then p {0, } and x = x W, x W. If π =, then p {0, } and x = x W, x W. Proof. π = reveals that θ = x W with probability one. So if x W = then p = 0 and x =,, while if x W = then p = and x =,. π = reveals that θ = x W with probability one. So if x W = then p = and x =,, while if x W = then p = 0 and x =,. Lemma x =, is not part of any pure strategy equilibrium. Proof. Suppose that x =, occurred in any pure strategy equilibrium. If the probability of victory for M in this equilibrium is not strictly greater than, M deviates to x = ; if it is strictly greater, then E deviates to Lemma 3 If x =, and π = 0, then p =, if, if + p q,, and x is equal to + p q, + 4] c, + p q [ + c 4,. Proof. Given x =,, x W = and π = 0 imply that either θ = and ω = with probability or θ = and ω = with probability p q. So p =, which is strictly greater than because p, q,. + p q u V E,,,, p = p p + c and u V M,,,, p = p p + ε then Pr[M wins,,,, p ] = Pr[ε c, ] = c Whereas, u V E,,,, p = p p + c and u V M,,,, p = p p + ε then Pr[M wins,,,, p ] = Pr[p + ε p + c] = Pr[ε 4p + c, ] = + 4p c = 4p 3 c Therefore, based on M s incentives,, is a mutual best response only if 4p 3 c c or equivalently only if p. But p > as noted above, so, cannot be sustained. We have just established that if p >, M prefers x =, to x =,. Obviously, M will always prefer x =, to x =, see Lemma and so M always chooses platform. Since u V E,,,, p = p p and u V M,,,, p = p p + ε then Pr[M wins,,,, p ] = Pr[ε 0, ] = It follows that E prefers x =, to x =, if and only 4p 3 c, or equivalently, p + c 4. Thus, an equilibrium with x =, exists if and only if p, + 4] c and one with x =, exists if and only if [ + c 4, ].

13 Lemma 4 If x =,, x W p q = and π = 0, then p = p q+ 0,, and x is equal to, if, if, if p q p q+ 0, 4 c, p q p q+ [ c 4, + 4] c, p q p q+ [ + c 4,. If x =,, x W = and π = 0, then p = + p q 0,, and x is equal to, if, if + p q p, + 4 c, + p q [ + c 4,. Proof. Given x =,, then x W = and π = 0 imply that either θ = and ω = with probability p q or θ = and ω = with probability. So p = p q p q+. u V E,,,, p = p p + c and u V M,,,, p = p p + ε thus Pr[M wins,,,, p ] = Pr[ε c, ] = c Whereas, u V E,,,, p = p p + c and u V M,,,, p = p p + ε + c thus Pr[M wins,,,, p ] = Pr[p + ε + c p + c] = Pr[ε 4p, ] = + 4p = 4p 3 Therefore, x M = is a best response to x E = if and only if 4p 3 c or equivalently if only if p c 4, and if it holds with equality M deviates by our indifference assumption. Since M has greater incentives to deviate from, than E, it follows that x =, is a second period mutual best response if and only if p < c 4. We have just established that if p c 4, M prefers x =, to x =,. Since u V E,,,, p = p p and u V M,,,, p = p p + ε + c so Pr[M wins,,,, p ] = Pr[ε c, ] = + c and it follows that E prefers x =, to x =, if and only 4p 3 + c, or equivalently, p + c 4. Thus, an equilibrium with x =, exists if and only if p c 4, + 4] c and one with x =, exists if and only if [ + c 4, ]. If we consider the situation where x =,, x W = and π = 0 imply that either θ = and ω = with probability or θ = and ω = with probability p q. Then p = and the second period best responses are as stated by an analogous + p q proof, with the corresponding p cutoffs, but noting that q > implies p > p. 3

14 Lemma 5 If x =,, x W p q = and π = 0, then p = p q+ 0,. If x =,, x W and π = 0, then p = + p q. In either case, x is equal to =, if p 0,,, or, if p =,, if p,. Proof. Given x =,, x W = and π = 0 imply that either θ = and ω = with probability p q p q or θ = and ω = with probability. Then p = p q+. Given x =,, x W = and π = 0 imply that either θ = and ω = with probability or θ = and ω = with probability p q. In the second period, neither party has an advantage, so the equilibrium consists of x E = x M = if p <, xe, x M {,,, } if p =, and xe = x M = if p >, where our indifference assumption on M rules out the other two options for p =. Lemma 6 If x =, and π = 0, then p = p q p q+, and x is equal to, if, if, if p q p q+ 0, 4 c, p q p q+ [ c 4, ], p q p q+ [, ]. Proof. Given x =,, x W = and π = 0 imply that either θ = and ω = with probability p q or θ = and ω = with probability. So p = p q p q+. u V E,,,, p = p p and u V M,,,, p = p p + ε thus Pr[M wins,,,, p ] = Pr[ε 0, ] = Whereas, u V E,,,, p = p p and u V M,,,, p = p p + ε + c so Pr[M wins,,,, p ] = Pr[p + ε + c p ] = Pr[ε 4p c, ] = + 4p + c = 4p 3 + c Therefore, x M = is a best response to x E = if and only if 4p 3 + c or equivalently if only if p c 4, and if it holds with equality M deviates by our indifference assumption. Since M has greater incentives to deviate from, than E, it follows that x =, is a second period mutual best response if and only if p < c 4. We have just established that if p c 4, M prefers x =, to x =,. Since u V E,,,, p = p p and u V M,,,, p = p p + ε + c 4

15 so Pr[Mwins,,,, p ] = Pr[ε c, ] = + c and it follows that E prefers x =, to x =, if and only 4p 3 + c + c, or equivalently, p. Thus, an equilibrium with x =, exists if and only if p c 4, ] and one with x =, exists if and only if [ + c 4, ]. Lemma 7 For any combination of first period platforms x = x E, x M then the following gives the first period pivotal voter s decision to vote M and probabilities of M winning x = x Vote M iff: Pr[M wins], ε > c + c, ε > 0 [ c + 4p 3, ε > c 4p if < p < c [ if p c 5, ε > 4p 4p if < p < ] if p 5 8 ] Proof. Note that we use this repeatedly that for any λ R, if λ Pr[ε > λ] = λ if λ [, ] 0 λ >.. We have four cases.. Case x =,. The voter utilities are: so that she will vote for M whenever u V M x E, x M, p = ε + c + p q = ε + c + p + q, and u V E x E, x M, p = p + q, ε + c > 0 ε > c. and so Pr ε > c = + c.. Case x =,. Then u V M x E, x M, p = ε + p q p q = ε p q, and u V E x E, x M, p = p q so the voter will vote for M whenever ε > 0, which occurs with probability. 3. Case x =,. Then u V M x E, x M, p = ε + c + p q = ε + c + p + q, and u V E x E, x M, p = p q, 5

16 and thus u V M x E, x M, p u V E x E, x M, p = ε + c + p + q + p q so that the voter will vote for M whenever and by, or equivalently, 4. Case x =,. Then { Pr[ε > c 4p] = ε + c + 4p > 0 = ε + c + 4p, ε > c 4p, if c 4p 4p + c 3 if c 4p [, ] { 4p + c 3 Pr[ε > c 4p] = if p [, 5 8 ] c 4 p [ 5 8 c 4, ] u V M x E, x M, p = ε p q and u V E x E, x M, p = p + q so u V M x E, x M, p u V E x E, x M, p = ε 4p + } }. 3 so the voter votes for M if and only if ε > 4p and by, { 5 Pr[ε > 4p ] = 4p if 4p [ ] 0, 0 if 4p } 4 or equivalently, { 5 Pr[ε > c 4p] = 4p if p, p [ 5 8, ] }. 5 Lemma 8 Strategy x M = strictly dominates x M =. Proof. Given x M =, P x E, x M + c strictly greater if E chooses xe =. If x =, then in the second period election, M can obtain at least a probability of winning in the second period by choosing the same platform as E, while if x =, then M can guarantee to obtain at least c by choosing the same platform as E. The table below summarizes a lower bound on M s utility: x E = x E = x M = + c + EP, P, + EP, with P, > + c, EP, and EP, c. So, P, + EP, > is a lower bound on M s total utility choosing x M =. Now, consider the choice of x M =. If E chooses x E = then the probability of M winning will be since no party has an advantage whereas if E chooses x E = the probability of M winning will be strictly smaller than since no party has an advantage and p >. If x =, then E can always guarantee herself at least a probability of winning in the second period by choosing the same platform as M, but this means that M can never get more than probability of winning in the second period. If x =, then E can always guarantee herself at least a probability of winning in the second period by choosing the same platform as M, but this means that M can never get more than probability of winning in the second period. The table below summarizes an upper bound on M s utility: x E = x E = x M = P, + EP, + EP, 6

17 with P, <, EP, and EP,. So, an upper bound on M s utility is + EP, which is less than the lower bound with with x M =. Proposition In any equilibrium, there exist functions Q p, c, Q p, c and Q p, c such that x =, whenever c 5 and { p, min Q p, c, q max Q p, c,, p or c > 5 and and x =, otherwise. p, min Q p, c, q max Q p, c,, q, p, min Q p, c, q Proof. We begin our proof by defining the functions below q + = + c p + cp ; q = c p cp ; and q = + c p cp Let P t be the equilibrium probability that M wins the election in period t, given x. Also, let ϕ = 4p + c 3. Then we have the following Lemma 9 If x =,, E[P ] = P = + c, and + p + q c if q p + p + q c + p q if q p, q+ + c if q > q+. If x =, and p 5 8 c 4, E[P ] = P =, and + p + q c if q q + p + q c + p q if q q, q + + c if q > q+. Finally, if x =, and p, 5 8 c 4, P = ϕ E[P [,, x ]] ϕ + p + q c + p q + ϕ q p c + p + q 3 if q, q and p < + c 4 ϕ + p + q c + ϕ + c p + if q, q and p > + c 4 ϕ + p + q c + p q + ϕ + c p + if q max{q, q }, q + ϕ + c + ϕ + c p + if q q +, 7

18 Proof. We consider the two cases x =, and x =, separately.. Suppose first x =,. From Lemma 6, P, = + c, and xw =. With probability, we observe π =, and then x =, and the probability that M wins the second election is + c. With probability p q, we observe π =, and then x =, and the probability that M wins the second election is. Finally, with probability p q + p q, we observe π = 0 and then from Lemma 6 and by studying the properties of q + we obtain the first column and the conditions in the following table: x P, + c if q p, p q, 4 p q+ 3 + c if q p, q+., if q > q + For the probabilities, the first and third row are immediate. For the second row, 6 So, M wins if which occurs with probability u V M x E, x M, p = ε + c + p q p q = ε + c + p + q, and u V E x E, x M, p = p q p q = q p. ε c p, c + 4p = 4p 3 c p q = 4 p q c. Thus, if q p, the expected utility for M in the second period is + c + p q + p q + p q + c = + cp + q ; if q p, q +, the expected utility for M in the second period is + c + p q + p q + p q p q 4 p q c = + cp + q q p; and if q q +, the expected utility for M in the second period is + c + p q + p q + p q = + c.. Suppose now x =,. Unfortunately, in this case we have eight separate subcases for different parameter p, q, c values in the parameter space,, 0,..a. Consider first three subcases corresponding to p 5 8 c 4. In this case, xw = so P = and p q we obtain posterior p, 0 = p q+. With probability, we observe π =, and then x =, and the probability that M wins the second election is + c. With probability p q, we observe π =, and then x =, and the probability that M wins the second election is c. Finally, with probability p q+ p q, we observe π = 0 and then we have three subcases depending on {q, c}, and 8

19 from Lemma 4 and by studying the properties of q and q + we obtain the first column and the conditions in the following table: x P, + c if q < q. p q, 4 p q+ 3 if q [q, q + 7 ],, c if q > q+. So, if p 5 8 c 4 and q < q, the expected utility for M in the nd period is = + c + c + p q c p q + = p + q c + ; c + [p q + p q] + c p q if p 5 8 c 4 and q [q, q + ], the expected utility for M in the nd period is + c + p q c p q + p q + p q 4 p q + 3 = + p + q c + p q; and if p 5 8 c 4 and q > q+, the expected utility for M in the nd period is + c = + c = + c. + p q c + c + p q + p q c.b. Now consider the five subcases in which p, 5 8 c 4. Then x W can be + or. Note u V E,, p = p p = p u V M,, p = p p + ε + c = p + ε + c u V M,, p u V E,, p = 4p + ε + c so Pr[M wins,, p] = Pr[ε c 4p, ] = + c + 4p = 4p + c 3. So, with probability 4p + c 3, xw = and then, subject to x W =, as noted in the proof for case.a., E[u M x =,, x W = + p + q c if q < q. + p + q c + p q if q [q, q + ], + c if q > q+. 9

20 On the other hand, with probability 5 4p c, xw = and then, subject to x W = : π x Probability {, + c} [, ] p q., if q q {0, c}, if q q + p q, {, + c},., 8 where p, 0 = + p q and the x outcome given π {0, c} is by by studying the properties of q and Lemma 4. Notice that the probability that M wins in the second period as a function of x given x =, is P [,,, ] = c, P [,,, ] = + c and given π {0, c}, P [,,, ] = Pr[ε + p > p ] = Pr[ε > 4p ] = 4p 3 = 4 + p q 3. So, subject to x W winning for M : =, we can update Table 8 to include expected second period utility probability of π P [,, x ] Probability {, + c} [ c p q. 4 {0, c} + p q 3 if q q ], 9 + p q, + c if q q {, + c} + c. Aggregating probabilities over all three events, we can calculate the expected probability of winning, not conditioning on π, as If q q, then P [,, x ] = p q c + + p q 4 + p q c = q p c + p + q 3, whereas if q q, then P [,, x ] is equal to = p q c = + c p +, + p q + c Recalling that q q +, and aggregating probabilities over the events x w = and x w =, we now have five subcasesas described in the lemma P [,, x ] if q 4p + c 3 + p + q c + 5 4p c q p c + p + q 3, min{q, q } 4p + c 3 + p + q c + p q + 5 4p c q p c + p + q 3 q, q 4p + c 3 + p + q c + 5 4p c + c p + q, q 4p + c 3 + p + q c + p q + 5 4p c + c p + max{q, q }, q + 4p + c 3 + c + 5 4p c + c p + q +, We can partition c, p, q space according lemma 9. We have nine potential regions: 0

21 . If q q +, then, will be preferred when or + c + + c ϕ + ϕ + c + ϕ + c p + q q = c cp ϕ + 4cp + cp. If p > + 4 c c or and q p, q + then, will be preferred when + c + + p + q c + p q ϕ + ϕ + p + q c + p q + ϕ + c p + q q = c + p + 3cp + ϕ 4p + 6cp + cp c + ϕ + c 3cp 3. If p > + c 4 and q q, p then, will be preferred when or + c + + p + q c ϕ + ϕ + p + q c + p q + ϕ + c p + q q 3 = c + p + 3cp + ϕ 6cp + cp c + ϕ + c 3cp 4. If p > + c 4 and q, q then, will be preferred when or 5. If + c 4 > p > + 4 c c or + c + + p + q c ϕ + ϕ + p + q c + ϕ + c p + q q 4 = c + 4cp + ϕ 6cp + c 4p ϕ + c 3p and q q, p then, will be preferred when + c + + p + q c ϕ + ϕ + p + q c + p q q q 3 + ϕ + c p +

22 6. If + c 4 > p > + 4 c c and q, q then, will be preferred when or 7. If < p < + 4 c c or + c + + p + q c ϕ + ϕ + p + q c + p q 8. If < p < + 4 c c or + ϕ q p c + p + q 3 q q 5 = c cp 3 ϕ + c 4p + 4cp + 5 cp + 4ϕ and q q, q + then, will be preferred when + c + + p + q c + p q ϕ + ϕ + p + q c + p q q q + ϕ + c p + and q p, q then, will be preferred when + c + + p + q c + p q ϕ + ϕ + p + q c + p q + ϕ q p c + p + q 3 q q 6 = c cp 3 ϕ + c + 4cp + 5 cp + 4 4ϕ 9. If < p < + 4 c c and q, p then, will be preferred when or + c + + p + q c ϕ + ϕ + p + q c + p q q q 5 + ϕ q p c + p + q 3 We can summarize all of this by saying that the dashed lines actually don t matter, so effectively, the c, p, q is partitioned in six areas. If q q +, then, will be preferred when q q. If q max p, q, q + then, will be preferred when q q 3. If q max q, q, p then, will be preferred when q q 3 4. If q, q then, will be preferred when q q 4 5. If q, minq, p then, will be preferred when q q 5 6. If q p, q then, will be preferred when q q 6 Although we also have the following that we provide without proof available upon request:

23 Lemma 0 If q p, q then q q 6. which implies that the restriction q q 6 is redundant. So now write { q if q q Q p, c = +, q if q max p, q, q + { q3 if q max q Q p, c =, q, p q 5 if q, minq, p Q p, c = q 4 then we get the result in the proposition if we note that case 4. above requires that q p, c = q 4 p, c for p > 4 + c 4 and this requires that c > 5 as claimed above. Finally, we get Remark 3 in the main text by noting that if ϕ = then q = q = Q p, c = 4c cp q 3 = q 5 = Q p, c = + 4p 4c cp q 4 = Q p, c = 4c cp c p and the result just follows by expressing these as a function of c. Proposition Q p, c and Q p, c are decreasing in p and increasing in c while Q p, c is increasing in p and decreasing in c. Proof. Simple inspection shows this to be true for the case p 5 8 c 4 where ϕ = and so q = q = Q p, c = 4c cp q 3 = q 5 = Q p, c = + 4p 4c cp q 4 = Q p, c = 4c cp c p Consider now the case p < 5 8 c 4 where ϕ = 4p + c 3.. dq dp dq dc = = d d pc +3p 8p 4c+ p cp dp pc +3p 8p 4c+ p cp dc = p c c cp < c c cp < 0 = p + c p c p > 0. As we know dq 6c dp = + 96c + 56 p + 3c 3 + c 64c 30 p + 4c 4 4c 3 59c + 44c c + 6p + 6cp + 4c p 0cp c 0 3