WHAT IS AN EXAMPLE?

But what exactly is an example? To begin, it is not a case (though it is not uncommon to see cases misdescribed as examples,Footnote ² and vice versa). Cases get studied, examples get adduced. It is easy to speak of a case study, while an “example study” makes little sense. An example is a specific manifestation of a general point.Footnote ³ The point in question might refer to a characteristic, practice, behavior, decision, structure, process, or relationship.Footnote ⁴

An example can be as short as a clause in a sentence, and as long as you like (so it is not length that distinguishes an example from a case).

Examples can be real or imaginary. In social and political inquiry, most examples are real.Footnote ⁵ Such examples should be verifiable, so we can be sure the author is not just making them up. A verified example will at a minimum constitute proof of possibility: the point at hand applies in at least one instance. But if an example is designed just to help understand an abstract point or fix a point in memory, then an apocryphal or even fictional story may be fine. Landemore’s (Reference Landemore2012, 97–9) example in her analysis of the problem-solving rationality of democratic interaction that integrates a variety of viewpoints is the jury in the film Twelve Angry Men. Made-up examples may also be fine if they are used to add some plausible values to a formal model, and thus help readers understand the model. So the prisoner’s dilemma is usually illustrated not with real interacting prisoners and prosecutors, but with imaginary ones (e.g., Hardin Reference Hardin1982, 2). For any imaginary or fictional example, one might perhaps ask why a real example is not available. There may be good answers: information on real juries is hard to come by because they deliberate in secret, real-world interactions of prosecutors and prisoners may involve too much complicating detail, and again take place behind closed doors.

WHAT IS AN EXAMPLE GOOD FOR?

Why do we use examples? In this section, I will introduce the six functions (clarifying, didactic, persuasive, universalizing, critical, and cogitative) listed above in the introduction. The subsequent six sections will expand on how to perform each of them well. These functions are not mutually exclusive, and specific examples may serve more than one of them.

The first and perhaps most straightforward function is a simple clarifying one: to enhance readers’ knowledge and understanding of a point. The point in question might be conceptual, descriptive, interpretive, explanatory, or normative. Nonobvious points are more in need of examples than obvious ones. I will be using examples for simple clarifying reasons at a second-order level throughout this paper, when I illustrate my own points with examples as used by other authors.

This first function is especially important when it comes to abstract points, and can help guard against readers’ misunderstanding of them. Formal theory deductions can be presented in abstract logical or mathematical terms; or they can be accompanied or even introduced through examples. The prisoner’s dilemma is normally introduced to the reader through an example with some specific characters (prosecutors and criminals) and payoffs (expected length of sentence for each prisoner) to help the reader comprehend the formal model. Axelrod (Reference Axelrod1981, 307, 309, 316), in a classic American Political Science Review article developing an iterated prisoner’s dilemma model to explain how cooperation can emerge among self-interested actors, comes back several times to the example of the development over time of reciprocity among U.S. Senators in an institutional setting that was once characterized by “falsehood, deceit, treachery” (Axelrod Reference Axelrod1981, 307; here Axelrod is quoting a 1906 observer).

The simple clarifying use of examples can also involve specification of the puzzle that the author wants to solve. For SoRelle (Reference SoRelle2023), again in the American Political Science Review, the puzzle is why borrowers and the consumer groups that ought to represent them fail to mobilize politically in the United States. To help establish this puzzle, she uses the example of consumer groups that mobilized 5,000 people to protest at a 2009 meeting of the American Bankers Association—but none for any action directed at government (SoRelle Reference SoRelle2023, 986).

The second reason to use examples is more didactic in its emphasis: to teach readers something they did not already know about the world. An American Political Science Review paper by Goldfien, Joseph, and McManus (Reference Goldfien, Joseph and McManus2023) uses formal modelling and a conjoint experiment to support its thesis that domestic policy decisions have a demonstration effect when it comes to how leaders in other countries view the resolve of the leader making the decision. However, the article begins with a vivid story about how in 1981 President Ronald Reagan’s firing of 11,345 striking air traffic controllers signaled his resolve to the Soviet Union. This example is intended to communicate the basic thesis of the article (as for the first reason), but it also teaches the reader something novel—if the thesis that the example contains were not novel, the article would probably not have been accepted for publication in the American Political Science Review.

The third reason to use examples is persuasive: to convince the reader that the author’s point is correct. Authors do not have an interest only in being clear and didactic; they also have an interest in being accepted as right. An example can constitute evidence that the point at hand is correct. Goldfien, Joseph, and McManus as just discussed have a thesis they want the reader to accept. Their formal model and their conjoint experiment should help persuade the reader, but the striking example of Reagan and air traffic controllers will also contribute. Indeed, it is conceivable that the reader will remember the example more than the model and experiment. Agent-based modelling involving algorithms and social networks might explain the formation of polarized filter bubbles and echo chambers in social media (Geschke, Lorenz, and Holtz Reference Geschke, Lorenz and Holtz2019); but a litany of examples will help convince the reader of the importance of these phenomena (Sunstein Reference Sunstein2009).

The fourth reason to use examples is universalizing in the sense of an ability to signal wide applicability of the author’s point. Wide applicability does not imply that the point applies to every relevant instance (which no finite set of examples can establish), but rather to many relevant instances. Wide applicability can be demonstrated through multiple examples (as I have just suggested for filter bubbles and echo chambers), and/or through finding some examples in unexpected places. Ostrom (Reference Ostrom1990) builds her explanation of cooperative management of common pool resources on multiple case studies—but before she gets to those, she lists at the outset a wide range of examples of situations to which the idea of a commons has been applied, including unexpected ones such as “the organization of the Mormon Church” and “communal conflict in Cyprus” (Ostrom Reference Ostrom1990, 3).

The fifth function of examples is critical, to call into question or refute a point. Critics of Duverger’s Law (that simple plurality electoral systems will yield a two-party system) could point to the counterexamples of several Latin American countries, India, the United Kingdom from 1910 to 1945, Quebec (all mentioned by Farr Reference Farr and Ball1987, 57), and the UK since the 1980s. Counterexamples will of course normally be introduced by critics. Sometimes, though, an author will introduce a seeming counterexample if they think they can refute it. Riker (Reference Riker1982, 760) in defending Duverger’s law argues that the apparent exception of Canada is not a true counterexample because it is only the result of strong regional parties, while the apparent counterexample of India leads Riker to reformulate the law to provide for an exception when “one party among several is almost always the Condorcet winner” (Riker Reference Riker1982, 761) (i.e., beats any other party in a pairwise vote).

Sixth and finally, examples may be cogitative in enabling the author (or authors) to reason through a point and reach more general conclusions. That is, examples can be used in thinking, rather than just in writing; to help the author (or authors) reach conclusions, rather than just illustrate them. This use bears some resemblance to how Kant in his Critique of Pure Reason saw examples, as wheeled “baby-walkers” (gangelwagen) that thinkers should use but then must discard as they mature and their judgment and reason improve, just as babies grow and can eventually walk by themselves and discard the walker. (For social scientists, my first five functions of examples suggest—against Kant—that they can usefully be retained after authors have reasoned points through.)

This cogitative function is hard to illustrate, because by the time the example is presented it will be with the audience rather than the author(s) in mind, and the author(s) will not generally commit the original thinking process to print. However, there are exceptions. Olson (Reference Olson1993) explicates his theory of state formation through reference to the figure of a stationary bandit, who (unlike roving counterparts) can benefit substantially from stability and prosperity in the local population. The stationary bandit has an incentive to secure local economic growth and (eventually) tax rather than rob, which is to the locals’ advantage too. Olson (Reference Olson1993, 568) says that this “answer came by chance to me when reading about a Chinese warlord”—which then helped Olson reason through why people everywhere should prefer the stationary warlord/bandit to the roving one, and (ultimately) prefer the state rather than anarchy.

To summarize, there are at least six functions of examples: clarifying, didactic, persuasive, universalizing, critical, and cogitative. None of these functions is unique to social science, and indeed the first clarifying one especially may permeate everyday talk. But we can think about the crafting and evaluation of examples in terms of how well these functions are performed in the specific demanding context of social and political inquiry. What facilitates good performance? In the six sections that follow I will examine each function in more depth with a view to determining how it might be done well by the author. These considerations also provide resources to readers to evaluate the adequacy of the author’s use. I then move to show how correction of the dangers accompanying examples may facilitate good collective inquiry.

A CLARIFYING EXAMPLE IS UNAMBIGUOUS, UNDERSTANDABLE, AND POSSIBLY TRUE

To begin with the first function, the straightforward clarifying one that involves facilitating knowledge and comprehension of a general point, we can ask how well the example truly embodies the point being made; and if it does so in unambiguous and understandable fashion. Examples ought to do this rather easily. The use of an example in presenting the prisoner’s dilemma as mentioned earlier embodies the point at hand almost by definition. More empirically, Esberg and Siegel (Reference Esberg and Siegel2023, 1363) illustrate their claim that antiregime dissidents who go into exile become more likely to seek foreign intervention if this coincides with the interests of their host nation’s governments with the examples of Iraqi (under Saddam Hussein) and Cuban exiles in the United States—which clearly do illustrate this point in understandable fashion. Mansbridge (Reference Mansbridge2003, 523) introduces the example of Representative Barney Frank and the workings of his office to explain “surrogate representation” of categories of people beyond the representative’s own constituency—in this case, “gay and lesbian citizens throughout the nation.” Again this helps communicate an abstract point.

While actually embodying the point might seem an easy test to pass, some examples can leave the reader wondering if they really do illustrate a point adequately. There are two ways to fall short here. The first is existential: is the point actually present in the example as presented? Axelrod’s (Reference Axelrod1981) example introduced earlier may indeed indicate that over time the U.S. Senate became less treacherous and more cooperative. But while he mentions several developments in Senate history that might be conducive to the evolution of the norm of reciprocity through the spread of a “tit for tat” strategy toward cooperation and defection that he thinks is key, the example does not actually include anyone explicitly adopting this strategy.

The second way to fall short is empirical, and occurs when the point is clearly present, but the example is not necessarily true to reality. Perhaps the most famous example of any point in the literature on environmental governance is the commons of a village as it appears in Hardin’s (Reference Hardin1968) “The Tragedy of the Commons.” Hardin argues that each villager in making a decision as to whether or not to put an extra cow on the commons will accrue all the benefits personally, while the costs of that extra cow in land degradation are shared with all the other villagers. Every villager is faced with the same decision, and as a result each will keep adding cows until the commons is destroyed. The problem with this example is that there is no documented case of this ever happening in real villages with commons, where commoners find ways to regulate access, as Ostrom (Reference Ostrom1990) later demonstrated so powerfully.Footnote ⁶ While some of the other empirical examples in Hardin’s article (such as fisheries) really do illustrate his thesis about how the commons gets degraded, one moral here is that the fact that a core example does not empirically manifest the point being made does not necessarily detract from the impact of your paper—there are over 56,000 cites in Google Scholar for this article. Irrespective of any failing in capturing an empirical manifestation of his argument, the example of the village commons clearly works in embodying his core thesis in unambiguous and understandable fashion. Given how often the example comes up in the literature on the commons, it is clearly also memorable; so memorable examples do not have to be true. The empirical failing could perhaps be forgiven if the example is read generously as counterfactual history: what would have happened without measures to control access to the commons, though this is not how Hardin presents it. Landemore’s (Reference Landemore2012) use of the jury from Twelve Angry Men to illuminate the epistemic superiority of democracy that I mentioned earlier shows that a memorable example can be explicitly fictional.

Examples that are already familiar to an audience may be more immediately understandable than those that are not. A familiar example should be more capable of triggering an immediate response, as the audience does not have to process everything about the example from scratch. This could help explain the popularity of recurring examples such as Martin Luther King, Jr. and the Cuban missile crisis in the literature (I will have more to say about both of these below): they are already well known to a political science audience. On the other hand, if an audience is familiar with an example that is then used by an author to illustrate an unfamiliar or novel point, that means the audience has resources to challenge this point. Hardin’s (Reference Hardin1968) example of the grazing commons should not impress an audience of agricultural historians.

A GOOD DIDACTIC EXAMPLE HAS A COMPELLING STORYLINE

For the second, didactic, function, teaching the reader something new about the worlds is facilitated by a compelling storyline. Relevant elements might include interesting character(s), clear identification of heroes and/or villains, an unambiguous and important outcome, or unexpected twists in the story. These ingredients help make an example memorable, by fixing the point the example illustrates in the reader’s memory.

The Goldfien, Joseph, and McManus (Reference Goldfien, Joseph and McManus2023, 609) example concerning Reagan and the air traffic controllers I mentioned earlier proceeds as follows:

This example really isn’t conclusive as a manifestation of the general point the authors want to make: it depends on reporting some impressions by a Reagan appointee (Allen) and Reagan supporter (Safire). The closest it gets to real evidence of what the Soviets thought is a second-hand report from an aide. What the example does have is a compelling storyline with an unexpected twist. It is not just those who lived in the United States in 1981 and remember Reagan’s actions who would probably never have thought of linking specific domestic actions to projecting resolve in foreign policy. (Though the storyline may be less compelling for a younger audience!)

Sometimes a compelling storyline is ripe for the picking in the service of any new point. The 1962 Cuban missile crisis has all the elements of a good story. It is dramatic in that the world was at the edge of nuclear war, the US had a charismatic president who convened a key advisory group whose tense and thoughtful exchanges are well documented. There are twists in the story as a lot turns out to depend on the actions of subordinate actors (some heroic, some dangerous) on both sides, with a clear (successful) outcome achieved in a matter of days. It has been analyzed many times over as a case study (Allison Reference Allison1971 is the classic treatment). But it is also extremely popular as an example.Footnote ⁷ Goodin (Reference Goodin2017) deploys the example in didactic fashion: to show that the epistemic argument for the superiority of deliberative group decision making depends on a good option actually being on the table (which might sound obvious, but was missing in earlier treatments). Early on in the deliberations of President Kennedy and his advisory Executive Committee, the blockade option eventually chosen was not even seriously present as an alternative.

A PERSUASIVE EXAMPLE WORKS AS RHETORIC

The persuasive function of examples, to help convince the reader that the author is right, can be analyzed in terms of rhetoric, for rhetoric is the discipline which studies persuasion in all its forms. Rhetoric can also help make a point memorable, and so is relevant to both the clarifying and didactic functions just discussed; a compelling storyline is an aspect of rhetoric. Hardin (Reference Hardin1968) has some striking rhetoric in his article that can be connected more or less closely to his core example of the grazing commons that I discussed earlier: “freedom in the commons brings ruin to all,” the only solution is “mutual coercion, mutually agreed upon,” “freedom to breed is intolerable.” These pieces of rhetoric are jarring and unsettling. Whether they help persuade the reader is a different question, but they certainly help grab the reader’s attention, and render Hardin’s points memorable.

Analysis of the rhetorical force of examples can begin through reference to Aristotle’s classic rhetorical principles of logos, ethos, and pathos. Logos is the most straightforward of these principles (but perhaps the least interesting for present purposes): it refers to the marshalling of pieces of evidence to support reasoning on a point. As such logos does not take us beyond what I said above under the clarifying function about evaluating examples in terms of how well they actually do embody the point being made.

Ethos refers to display of the excellence of character of the speaker/writer that should invoke trust on the part of the audience. Good rhetoricians always work with a knowledge of the dispositions of their intended audience. One indicator of excellence of character concerns the positive and negative examples that the speaker chooses, and with which they implicitly associate themselves. For an audience of political scientists, a discipline whose members’ center of gravity is liberal-progressive (Rom Reference Rom2019), Martin Luther King, Jr. and Nelson Mandela are clearly admirable leaders; Donald Trump is clearly not. So if you want to illustrate effective leadership, choose King or Mandela. Trump should be reserved only for negative examples. If you want to illustrate innovative or effective social movement activism, choose La Via Campesina (Deveaux Reference Deveaux2018), Black Lives Matter (Nepstad Reference Nepstad2023, 8), Occupy (della Porta Reference della Porta2015, 2) or Extinction Rebellion, not the Tea Party or MAGA, let alone Proud Boys or Oath Keepers.

To further establish the importance of ethos in the selection of examples, consider the popularity of Martin Luther King, Jr.’s leadership as an example. But what is his political activity an example of? It turns out to be many things, including:

• • The importance of performance (as opposed to deliberative argument) in political action; the key to his success is in performing civility and nonviolence in the face of violent intimidation (Alexander Reference Alexander2006, 312).

• • Deliberative representation of the disadvantaged (Gutmann and Thompson Reference Gutmann and Thompson1996, 133).

• • The need for social movements to act nondeliberatively and coercively (Medearis Reference Medearis2005, 55).

• • Religious appeals that cannot easily be accommodated in deliberation as generally conceived (Medearis Reference Medearis2005, 63).

• • A brilliant rhetorician who could reach Americans of all races through emotional appeals about justice and who “universalized his normative claims by tapping into the particularity of the American creed and its ideals” (Triadafilopoulos Reference Triadafilopoulos1999, 754).

• • An irreplaceable leader, “whose highly personal leadership… could not after his assassination be effectively transferred” (Burns Reference Burns1978, 267).

• • A leader who insisted he was a replaceable “cog” in a social movement: “Martin Luther King, Jr., for example, was always at pains to emphasize that he was dispensable and that the civil rights movement would go [on] without him, should he fall by the wayside.” (Goodin Reference Goodin2023, 1402).

Could King really exemplify all of these things, some of which are apparent opposites? It is possible that he could, perhaps at different times, so there is nothing necessarily wrong with the way the authors use him as an example. The point I want to make here is a bit different (and would hold even if every one of the dot points were correct). It is that King is a good example because (at least for a political science audience) he is a moral hero, not in light of anything stemming from the social scientific commitments of political scientists, but because of the liberal/progressive political disposition of most people in the discipline. So using King as an example to illustrate any point—rather than (say) Donald Trump, another leader who mobilized people effectively through the power of speech—helps establish the ethos of the writer/speaker by establishing an association with him. This could help explain the sheer frequency with which King crops up in examples. The term “virtue signaling” is generally used by right-wing critics as a put-down of progressives, otherwise I might use it here as a synonym for this use of ethos.

Ethos might also be established by the erudition associated with an example. So rather than choosing an example from contemporary politics, it might be better to reach back, to demonstrate the author’s command of history (even though the history itself may be of no broader relevance to the inquiry at hand). This perhaps explains the popularity of examples from the ancient world in thinkers as different as Machiavelli (Dienstag Reference Dienstag2017) and Hobbes (Tourneux Reference Tourneux2021). They could establish an ethos of erudition through their command of history, even if that was not their intention.

Pathos refers to emotional appeals. One way of getting an example to resonate in the reader/listener is to get an emotional response. The emotion in question might be sympathy with the downtrodden or those struggling to do the right thing, admiration of those who overcame odds to flourish, anger or outrage at injustice, disgust at corruption, delight at an unexpected positive or negative turn, empathy with the tough situation of others, or amusement. There is an overlap with what I just said about ethos here. So Martin Luther King, Jr. might elicit an emotional response of sympathy and admiration (even if it is not explicitly invoked in the use of the example): he was someone willing to risk and eventually give his life for his cause. If so, using King as an example is particularly powerful, because it works in both ethos and pathos terms. Jarring rhetoric may seek to provoke an emotional reaction against the author as a way of getting the reader’s attention—see my earlier observation on Hardin’s (Reference Hardin1968) “freedom to breed is intolerable.”

A particularly effective emotional response might be induced by Saward’s (Reference Saward2009, 1) opening of an article on the legitimacy of claims made by unelected representatives with a quote from the musician Bono. Referring to his work in pressuring donors to do more to help the poor, Bono said: “I represent a lot of people [in Africa] who have no voice at all… They haven’t asked me to represent them. It’s cheeky but I hope they’re glad I do.” This example works at the level of logos because it is indeed a very explicit representation claim by someone who is self-appointed. When it comes to ethos, Bono is an overprivileged celebrity behaving arrogantly, hardly an admirable figure with whom to be associated, in this context. However, the reader could be induced to share disdain for Bono’s arrogance, which would in itself help establish ethos for Saward. At the level of pathos, the example might invoke an emotional response of either amusement or outrage, given that Bono’s claim is on the face of it preposterous.Footnote ⁸ This example took on an extended life in the representation literature—Dryzek and Niemeyer (Reference Dryzek and Niemeyer2008) begin their paper on discursive representation with Bono too,Footnote ⁹ interpreting him as a representative of a particular (problematic) discourse, one that treats Africans as poor recipients of charity with little agency of their own. The same quote becomes a key example for Montanaro’s (Reference Montanaro2012, 1096) treatment of self-appointed representatives, and appears frequently in other treatments of problematic representation claims (Mulieri Reference Mulieri2013, 519; Minami Reference Minami2019). There was a panel at the 2008 annual conference of the American Political Science Association entitled “Bono and Beyond: The Democratic Functions of Non-Elected Representatives.”

One further twist to the story is that Bono also became the target of a citizen campaign to “make Bono history,”Footnote ¹⁰ which Dieter and Kumar (Reference Dieter and Kumar2008, 263) use as an example of pushback against celebrity diplomacy. This was a play on his identification with the “make poverty history” slogan. “Not about us without us” became a popular alternative slogan for developing country activists reclaiming agency and opposed to the kind of celebrity activism that Bono exemplified (Brassett and Smith Reference Brassett and Smith2010, 426), casting further doubt on the validity of Bono’s representation claim.

Pathos in the use of examples can extend to the neoliberal right of the political spectrum, where one is more likely to find some economists than political scientists. Horror stories about government failure can be deployed to help confirm the case against active government in general (not just the issue at hand). Anderson and Leal’s (Reference Anderson and Leal2015) Free Market Environmentalism is peppered with stories about bad results from government policies, including government subsidy of forest destruction (as well as government overprotection), subsidy of water-intensive crops in the desert, fish kills resulting from too much water going to irrigation, and so forth. The stories may well be true, and so work at the level of logos. But their power is reinforced by the emotion of outrage they are likely to engender in a neoliberal audience, and help induce extrapolation from the specific example of government failure to government in general. This is of course what neoliberal politicians can do—as when Ronald Reagan invoked “welfare queens” to justify cutbacks in government welfare programs. While there was indeed one real person who fit the description Reagan had in mind (see Levin Reference Levin2019), the idea was to elicit emotional response that implicated all recipients of welfare.

UNIVERSALIZATION IS SIGNALED BY MULTIPLE COMPELLING EXAMPLES

If one example is good, then on the face of it many examples that truly embody the point at hand might be still better. The use of multiple real examples may guard against giving the impression that what an example is designed to illustrate is in fact rare. The use of a single obscure example runs this risk. Chapman (Reference Chapman2023, 959–60) illustrates the idea that “governing parties can introduce new dimensions that scramble political debates” in order to (say) distract voters from their poor economic performance with an example from the 1987 New Zealand general election. This example may work well as a matter of logos; but it may be obscure to most readers of the American Political Science Review (where the article appeared), so risky in these terms.

Multiple examples can also underwrite a distinctive method of inquiry. This is how Machiavelli constructed his generalizations about politics, trying to draw universal lessons from the patterns that could be found in an accumulation of many examples from different times and places (Dienstag Reference Dienstag2017, 485–6). For Machiavelli, “Not only was reliance on a single case dangerous, but the accumulation of examples made patterns visible that could not otherwise be discerned.” (Dienstag Reference Dienstag2017, 486).

Multiple examples can also be put in the service of an essentially deductive explanation. In his presentation of the tragedy of the commons, Hardin (Reference Hardin1968) as discussed above quickly follows up the grazing commons with fisheries, free parking, access to national parks, air and water pollution, decisions about having children, even bank robbery (to explain why a bank shouldn’t be treated as a commons). His range of diverse examples suggests the wide applicability of his theory of the commons—and all of them do manifest his thesis. Goodin (Reference Goodin2023) is Machiavellian in the number and historical reach of the examples he deploys, but they are all designed to drive home his new solution to the old problem of collective action: why would rational individuals contribute to the provision of a collective good, if their own contribution is costly while making little difference to the outcome? Goodin wants to establish that the inconsequentiality of individual action that is generally seen as the cause of collective action problems is actually the solution to those problems. This is, to say the least, unexpected and jarring to those familiar with the literature. His explanation has two key elements.

His first point is that “people like to be associated with winners” (Goodin Reference Goodin2023, 1401). Goodin’s examples come from level of support for baseball teams that draw bigger crowds when they are winning (1401), and Martin Luther King, Jr. “telling his followers that they were backing a winner” because they were on the right side of history (1402).

His second key point is that multiple, redundant members or “cogs” are conducive to winning, and to social movement success. His examples include participants in the “Peterloo” rally for electoral reform that led to a massacre in Manchester in 1819; mass production of muskets with interchangeable parts in 1785; redundant backup systems in aircraft and spaceships; Martin Luther King, Jr. (again) saying that if he was killed, others would take his place; and an African-American teenager at a county courthouse in the American South in the 1960s trying to register voters saying if he was shot, “there are people coming from all over the world” (1403).Footnote ¹¹

As a matter of logos, the sheer multiplicity of examples does not constitute proof for a point, because there is always a danger that selection is ad hoc (as Dienstag Reference Dienstag2017, 495 points out when it comes to Machiavelli) or biased cherry-picking. Beyond demonstrating the broad applicability of a point, multiplicity can also be understood in rhetorical terms: repetition can be an effective rhetorical device. Multiplicity can also help in establishing the author’s ethos, demonstrating their command of relevant information.

CRITIQUE CAN BENEFIT FROM MULTIPLE COUNTEREXAMPLES

Counterexamples can be effective weapons of choice for critics of a point. Counterexamples should on the face of it be powerful. For it might seem that while no number of positive examples can prove a claim, a counterexample can falsify it. But falsification here would apply only to the degree a claim ostensibly embodies a universal law; such laws are of course rare in social science. The democratic peace thesis (democratic states do not go to war against each other) is not rendered false because we can think of a few examples where democracies have gone to war against each other, such as India versus Pakistan in 1999. One counterexample—or even a few—does not refute a theory, normally all it does is demonstrate the need to explain why the theory does not apply in the example at hand (Dowding Reference Dowding, Peters and Fontaine2020). Such explanation may need to involve investigating the example as a case. So the 1999 war could be explained on the grounds that Pakistan was a weak democracy with heavy military influence on government, certainly not a consolidated liberal democracy (Tarzi Reference Tarzi2007, 51).

Just like examples, counterexamples can be evaluated in terms of whether they really do contradict a point in clear and understandable fashion, whether they teach us something unexpected via a compelling storyline, and whether they are persuasive. Multiplicity is especially powerful when it comes to the deployment of counterexamples. Duverger’s law as introduced earlier suffers grievously under the weight of the sheer number of counterexamples that have been found. Defenders of the law might try to refine it to explain away the counterexamples—as Riker (Reference Riker1982, 761) did for India, which led him to build an exception into the law for cases where one party is always a Condorcet winner (see above). But each time this happens the law becomes more complicated and qualified. Multiple counterexamples cannot falsify a law, but in inducing complications (such as Riker’s) they can render the research program it reflects “degenerative” in Lakatos’s (Reference Lakatos, Lakatos and Musgrave1970) terms, and so ripe for abandonment. Duverger’s law now appears to apply unambiguously only to the single case of the United States, otherwise it may well be a “dead parrot” (Dunleavy Reference Dunleavy2012; see also Dunleavy and Diwakar Reference Dunleavy and Diwakar2013).

Multiplicity in counterexamples can also be deployed to criticize any author who follows Machiavelli in trying to establish the generality of their point through multiple examples. Returning to Goodin (Reference Goodin2023), it is possible to think of counterexamples to his first point about people liking to be associated with winners. For people do often join social movements with little chance of winning in any short term: be it in abolishing nuclear weapons, preventing further climate change, or stopping the slaughter of animals. Goodin’s examples therefore show only that some people like to be associated with winners, but we have no way of knowing what proportion of the relevant population is like this. When it comes to the second aspect of Goodin’s argument about replaceability, I have already noted Burns’s (Reference Burns1978) treatment of Martin Luther King, Jr. as irreplaceable.Footnote ¹² We might also note all the populist demagogues who have motivated their followers by presenting themselves as unique and so irreplaceable. (e.g., Silvio Berlusconi in 2008: “I am, in a word, irreplaceable.”Footnote ¹³) The whole idea of charismatic leadership as identified by Weber ([1921] Reference Weber1968, 215) is that political authority rests on “devotion to the exceptional sanctity, heroism or exemplary character of an individual person,” and Weber and others have been able to identify numerous examples, from Cleon of Athens to Napoleon to Benito Mussolini to Donald Trump.

The critical use of examples can also involve interrogating whether an example as presented by an author really does contain the point (as I did above for Axelrod’s history of the U.S. Senate), and if so whether it is true empirically (again see my earlier discussion of Hardin’s example of the grazing commons).

COGITATION BENEFITS FROM SERENDIPITY, DISCIPLINE, AND OPENNESS

The cogitative function uses examples for thinking rather than writing, and to help reach conclusions rather than help communicate them. This function is the one that is hardest to examine and illustrate, because the reader is not normally given access to authors’ thought processes (or discussions with co-authors). Perhaps Hardin (Reference Hardin1968) used the example of the village grazing commons to reason through key points of a general argument about the tragedy of the commons—but perhaps he didn’t. Perhaps contemplating Bono enabled Saward (Reference Saward2009) to think through the precepts of legitimate unelected representation—but perhaps not.

Olson (Reference Olson1993) is very much the exception here. His account of how coming across the story of a Chinese warlord enabled him to think about the figure of the stationary bandit and its role in state formation (introduced earlier) would suggest there is a role for serendipity, so the author should be receptive to this. The author should however exercise some discipline and not be seduced by the particularities of an example into rushing too quickly into thinking that no further proof of the point it embodies is required. Generalization from a single example is a bad heuristic. This means asking exactly what the example teaches us, and whether we can find other examples that do the same, or something similar, or something different. Olson (Reference Olson1993, 569) gives the impression he rushed (too) quickly to generalization: “History until relatively recently has been mostly a story of the gradual progress of civilization under stationary banditry interrupted by occasional episodes of roving banditry.” But we do not know if in his own thought he considered multiple examples on the way to this generalization. If I may be forgiven an autobiographical moment here: the idea for this paper came to me through wondering about the frequency with which the specific example of Martin Luther King, Jr. comes up in the literature, suggesting there might be something attractive about this example that is independent of the various points it is used to illustrate. This then led to a search for other popular examples, what might explain their popularity, and eventually the paper you are reading.

If the example helped the author(s), then it is reasonable to suppose it should also help an audience—and so be opened for public view when that audience enters to read or hear the argument. However, this is not essential, if the author(s) eventually thought of better examples than the one that initially helped them.

The six functions of examples and the corresponding ways to pursue them are summarized in Table 1.

Table 1. The Functions of Examples and How to Perform Them

THE DANGERS OF EXAMPLES

Examples can be linked to storylines in their didactic function, and to the rhetorical devices of ethos and pathos in their persuasive function. I have also noted the lesser degree to which rhetoric can enter into examples in their clarifying function (by helping to make an example and the point it embodies memorable), in their didactic function (if a compelling storyline is seen in rhetorical terms), and in their universalizing function (because repetition is a rhetorical device). In addition, both storylines and rhetoric can sometimes feature in counterexamples (reflecting the ways they can enter examples). Any linking of examples to storylines and rhetoric should immediately arouse the suspicion of those who follow Plato (and Hobbes) in believing that rhetoric should be banished from rational inquiry, on the grounds that all it does is enable people to mislead and deceive their audience (and possibly themselves).

Whether it is done intentionally or not, an audience might be misled by the use of examples that resonate but have a weak factual basis. The literature on social media and politics is full of examples of filter bubbles and echo chambers that detach their participants from the larger public sphere, often in extremist directions (notably, Sunstein Reference Sunstein2009). But Bruns (Reference Bruns2019, 1) surmises there is hardly any evidence here that holds up, and that “social media users generally appear to encounter a highly centrist media that is, if anything, more diverse than non-users.” Vivid examples may lead an audience to misperceive the frequency of a phenomenon. Think of the degree to which the examples of Trump in the United States and heads of government in Hungary and Turkey are invoked to illustrate the danger of democratic retreat (e.g., Mounk Reference Mounk2018, 2; or Runciman Reference Runciman2018, whose only example in the first few pages of his preface is Trump). This may induce in the audience an exaggerated perception of the degree to which backsliding has happened in most liberal democracies—most of which have not in fact allowed authoritarians like Trump, Orbán, and Erdogan to operate the levers of power.

EXAMPLES, FAST AND SLOW

To redeem the use of examples in light of the dangers associated with their capacity to mislead, it is possible to draw on Kahneman’s (Reference Kahneman2011) distinction between system 1 (fast) and system 2 (slow) thinking, as a way of systematizing the difference between relatively shallow and relatively deep thinking.Footnote ¹⁴ System 1 is low-effort, largely intuitive, dealing in immediate associations, and deploying heuristics—one of which is overgeneralization from a single example. System 1 is necessary because of the vast number of decisions that have to be made by everyone—including time-poor political scientists. Most of the time system 1 works pretty well, and indeed makes it possible to navigate life. The heuristics of system 1 may work better than system 2 for many or even most decisions (Gigerenzer and Todd Reference Gigerenzer and Todd1999). System 2 requires more time, effort, concentration, and reflection, and so is invoked relatively rarely. System 1 pervades everyday communication, including that of social scientists. But system 2 is absolutely central to any intellectual inquiry—including social science.

On the face of it, to the degree it effectively deploys ethos, pathos, and/or compelling storylines and repetition, rhetoric operates initially at the level of system 1—because the main point of rhetoric is to be striking and invoke immediate resonance in the listener or reader.Footnote ¹⁵ If we care only about how well an example works to persuade, then it is possible to evaluate its effectiveness solely in system 1 terms: does it trigger unreflective acceptance of the point it illustrates in the reader/listener?

However, that cannot be the whole story, because in the end, as an academic enterprise, political inquiry has to reach judgments using system 2. We can evaluate the effects of examples as contributions to political inquiry in terms of how they affect system 2. This includes the way Kant as discussed above saw examples: as aids to get us to the position where we think more deeply (though I will discuss other ways that examples can reach deep thinking).

One (non-Kantian) way of thinking about this connection involves asking whether what works at system 1 could also pass a system 2 test. Referring to technical communication, House and Livingston (Reference House and Livingston2013, 3) argue that “the communicator’s system 1 techniques must deliver the conclusions that system 2 would reach if the audience were to engage its processes.” In this light, an example that resonates in system 1 should be an effective shortcut to what would have been reached by system 2, were system 2 to be invoked.Footnote ¹⁶

This test does though imply that the example substitutes for system 2 thinking in the reader/listener; and that may be fine for the time-poor political scientist skimming an article or half-listening to a talk while multitasking on their phone. But to be redeemable from the point of view of inquiry in general, an example should be capable of more than this. Examples ought to be able to link systems 1 and 2 effectively. From the point of view of system 2, this link is inescapable: as Kahneman points out, system 2 can only work with inputs from system 1. In this light, a striking example should trigger a response that it is important and memorable enough to be an input to further (system 2) thinking. If it resonates and/or works in rhetorical terms, then that could make it more likely to be taken up by system 2 (rather than short-circuit system 2). But note the fact that it is flagged as important enough to be taken up does not mean it actually will be taken up.

This kind of linking of systems 1 and 2 is exactly what thought experiments (embodying examples) in moral philosophy can do by design.Footnote ¹⁷ They are designed to trigger an immediate response, which the author then argues helps establish a general ethical point. Perhaps the most famous such example is Singer’s (Reference Singer2009) drowning child. According to Singer, if you see a child drowning and can rescue them at little cost to yourself, obviously you should do it—the reaction sought is a system 1 immediate response, “it’s obvious.” But then Singer draws the reader into system 2. If you would save the drowning child, then to be consistent with the implicit moral principle you have followed, if you have a decent income or wealth, you should devote a large proportion of it to saving lives by donating to effective charities.

How does this sort of link look when it comes to political science? I am not suggesting political science follow moral philosophy in carefully constructing (hypothetical) examples, whose broader implications then invite interrogation. It is much less compulsory than it is in moral philosophy for readers/listeners always to move immediately to system 2. But a political science example can be scrutinized in terms of whether it could facilitate such a link (even if time-poor readers/listeners do not actually make it).

In my earlier discussion of Goldfien, Joseph, and McManus (Reference Goldfien, Joseph and McManus2023) on domestic decisions signaling foreign policy resolve, I noted the compelling storyline in its opening example. I also commented on the apparently weak evidence contained in the example. Does any dissonance between storyline and evidence induce readers to move to system 2, perhaps by studying the argument of the rest of the article? Answering that question would require surveying readers. I cannot think of any way of doing this that would not itself induce system 2, because it would require those surveyed to think more deeply about the example and article. But perhaps it is because the storyline is compelling, while the embodied evidence (at least in my eyes) fails to establish the point the authors want to make, that induces a need to dig further. I also commented on the existential weakness of Axelrod’s (Reference Axelrod1981) example of the evolution of cooperation in the U.S. Senate, and the empirical weakness of Hardin’s (Reference Hardin1968) grazing commons.

So does this suggest that from a social scientific point of view, the best examples are ones that are actually problematic in some communicative or rhetorical aspect, but good in others? It would be more appropriate to say that the best examples are ones that are good in some aspect, but flawed in interesting ways in other aspects. (Again this is very different from moral philosophy, where designers of thought experiments try to eliminate flaws.) It is not interesting that an example contains no ethos or pathos. It is interesting if it works on ethos and pathos, but has subtle failure in either logos or storyline. This does not mean that the author should deliberately build in such failure: because any “good” and “best” judgments here are from the point of view of the practice of social science, not the interests of the author in being compelling or persuasive.

As I noted earlier, Saward’s (Reference Saward2009) and others’ Bono example seems to work in terms of logos, ethos, and pathos. There is also a striking storyline: here is an overprivileged celebrity seemingly claiming to represent the poor from across a continent. But the example works precisely because it is an example of an illegitimate representation claim: on the face of it, it seems to contradict the idea that representation claims by the unelected can have democratic legitimacy. Thus, there is a subtle failure at the level of logos, which as an illustration of a representation claim is along the lines of “yes, BUT” rather than “yes.” While what Bono says is a representation claim, it is a bad one – suggesting the reader needs to think a bit more deeply (move to system 2) about why it doesn’t work, and so presumably what could work. And irrespective of what it does for these authors’ interest in being persuasive, from the point of view of advancing political inquiry (requiring system 2) the example is superb.

Counterexamples are particularly important from the point of view of system 2, because they can sow doubt in an audience. From the point of view of an author trying to persuade the audience of the veracity of a point, that is hardly to be welcomed. But from the point of view of inquiry in general, that can be positive, because it means that system 2 will need to be invoked to weigh the relative power of example and counterexample.

WHY NO PERFECT EXAMPLES

I have suggested that from the point of view of the discipline (and the invocation of system 2), the best examples may be those that are flawed in interesting ways. The author’s interest in persuasion may still lead them to search for a perfect example. A truly perfect example would fully substitute for further analysis: it would convince the reader thoroughly, on its own. Such an example would be understandable and memorable, embody a compelling storyline with an obvious moral, and persuade when it comes to logos, ethos, and pathos. It would not falter when confronted with alleged counterexamples.

Can we find a perfect example like this in political science? I invite the reader to try, but I do not think a truly perfect example could ever be located. There may be uncontroversial examples—such as mentioning that Scandinavian governments are examples of consensual political systems. But examples of this sort teach us little, they have little rhetorical force, no compelling storyline, no ethos or pathos. It is only in moving beyond uncontroversial points that the force of examples matters: clarifying, teaching, and persuading are necessary precisely because the point at hand is not absolutely and immediately convincing. A perfect example might suggest that further analysis (i.e., social science) is unnecessary, because it is clear from the example exactly what is going on, and that could explain the rarity and perhaps nonexistence of perfect examples. We need to do social science precisely because it is not obvious what is going on. It might be possible to imagine a future in which general laws of politics were established such that we knew exactly how every relevant example illustrated a law; but such laws continue to be elusive.