Even more fundamentally, the statistical and comparative methods are fundamentally different orientations to social science research (Frcndcris, 1983; Ragin, 1987). The comparative depends upon the careful a firiori selection of [lie cases. If we return to the fundamental litany of research design - maximise experimental variance, minimise error variance and control extraneous variance - then tlic comparative method depends upon the initial selection of cases to aciiicve those goals of research design. The cases must be selected in such a way as to control known sources of extraneous variance. This research method is therefore often inaccurate and incomplete; if we knew all the sources of extraneous variance in advance tlien there might be tittle need to do tlie research. Still, if care is taken in the selection of cases then there is some greater hope of achieving control.
Statistical analysis, on the other hand, generally is wilting and even anxious to include all available cases, and (lien use a variety ofex-posi statistical techniques to attempt to determine tlic impact of extraneous variables. This is a slight overstatement, but not by much. The canons of statistical methods seem to always push for more cases, given that tlicy can be seen as part of tlic same population of cases. Statistical iccliniques have tlie virtue of being more independent of the selection of the cases, but even so, if tlie appropriate data arc not collected then there is no way in which to determine the sources of tlie extraneous variance. Further, if some countries are systematically excluded because of poor quality of data then another source of extraneous variance may be introduced. Looking at tlie outliers in a regression analysis may enable the identification of the geographical source of the variance, but often not the variables producing the deviations from the neatly devised theory of the researcher. This potential problem also points to (lie need for substantial descriptive knowledge of llic cases being studied, even in a statistical analysis. Without dial sort of substantive knowledge, identifying why country X is an outlier, and choosing variables to use for a subsequent test for the fundamental source of extraneous variance, can become little more than an academic lishing expedition. Of course, no researcher can know about all relevant countries, but as comparativists we abandon our descriptive studies in favour of being 'high lecli' at great peril to any real understanding of countries and political dynamics.
Both tlic comparative method and tlie statistical method depend upon tlic ability to identify, ex ante, (lie potential sources of extraneous variance in tlie research question. If a comparative analysis does not identify tliose potential sources of confounding variance when making

the initial selection ofihe cases the researcher will not likely be able to recover and create adequate research later. Tlic consequences will be results lhai are confounded by the unmeasured characteristics of the cases selected for the 'sample'. Th? statistical method, likewise, may have its results confounded in an o^^ irretrievable manner by ihe failure to identify, and measure, itnport.uit correlalcd variables- A statistical researcher does have clx-slight advantage of being able to rerun the analysis with the previously unidentified variable included. The identification of [lie crucial ^measured factors may, however, require waiting for new thcoreticil development and a substantial passage of time. This delay may noibe as serious in the social sciences as it might be in medicine or the na^al sciences, but it may still lead
researchers and even practitioners down false and/or unproductive lines of enquiry.
In addition to the theoretical considerations that may argue for a smaller and more focused analysis, t^ere are always practical research questions. Unless there is aggregate yata - for example, budgets or voting data - readily at hand, Klanvely few social scientists can afford to collect extensive data over 3 large range of political systems. There have been a number of stu^s of this type historically, but fewer have been'completed recently. There are some exceptions to that generalisation, for example, die huge and detailed data-sets compiled by Barry Amcs, first on Laiin American budgets (1987) and then on Brazilian public expenditure (1996), and the massive study of public opinion in Western cou^ies titled Beliefs in Government (Kaase and Newton, 1995), but they have been few. Further, even if extensive data collection in a nuinbtr of countries is feasible economically, it may still not be the best usc^f scarce resources " temporal as well as financial - for the rcsearcf^. The fundamental questions must always be, What does a researcher gain from adding another doy.en cases, or even adding a single case, lo the sample? And, Does that case add anything to (lie argument and the ability to reject
theoretical propositions, or is it simpiy just another data point for the analysis?
This chapter addresses the import 'Goldilocks question' of just how many cases arc sufncient for endive comparative analysis. The previous chapter addressed one asp^ of the case selection question by asking whether (he cases selected should be most similar or most different, and further, on what du^^io,.^ i^y .should be most similar or diHerent. This chapter will extend that set of questions by looking at the quantitative dmiensio,^ j, iyi;iy appear excessive to

The lumber of Cases 61
have iwo chapters concerned with die selection of cases, but in some
ways case selection is (lie crucial question in the design of comparative research design - first, how many cases, and then which ones? It may be that more cases arc, on average, better, but more cases may merely be a compensatory mechanism for tlie poor selection of a smaller number of cases. As willi so many things in this field, there is no single correct answer as to wliat is the right number of cases - the only real answer is that 'It depends.'
Strategies with Different Numbers of Cases
The remainder of this cliaptcr is an examination of strategies available to the researcher wlio is faced with the possibility of using different numbers of cases. This choice could also be expressed in oilier ways, given that we have been arguing throughout that theoretical questions should guide the selection of cases, including both the number and the particular cases. The theoretical issues can lead to a choice of the appropriate number of cases, but there remain questions oljust how those cases are to he investigated, and what can be done to maximise the tlieorctical utility of the research. Further, there are some instances in which there is simply a possibility of only using a very small number of cases. If, for example, a scholar wants to examine successful democratic governments in Africa, the range of possibilities is unfortunately very limited at present (Picard and Oiirrity, 1994; Molutsi and Holm, 1990).
One Case
It is indeed possible to do comparative research of a sort with a single case. This statement appears to be almost a contradiction in terms, but the seemingly impossible can be done successfully in several ways, and for several reasons. The reasons for choosing this particular route for comparative research are more important tlian llie particular manner in which the research will be done, although the two issues niay lie closely related in practice. We should also be cognizant that another of the social sciences, anthropology, lias developed primarily through [lie accretion of case after individual case, each one developed and considered individually. Although perhaps less directly concerned with the process of comparison llian either political science or sociology (liul -see Naroll and Coln-ii, l']73), anthropology is

certainly a comparative social science and has developed most of its theory through (lie accumulation of case evidence. Although often seen as alhcorctical ;md purely descriptive, if it is well done then case-analysis can, paradoxically be one of the more theory-driven forms of
comparative analysis.
One primary reason for attempting to do comparative research
with only a single case is 10 utilise a very particular case to characterise a phenomenon lliat appears to be especially apparent in tliat one case. The single case therefore becomes a pre-lheorcticai exercise, leading, il is hoped, to a general si.iteiiifin about (lie phenomenon; tins strategy is what Richard Rose (1991: 454) calls ihe 'extrovertcd case-study'. The researcher lias identified, or believes that lie or slie has identified, an important exception to the prevailing theory, or a case which demonstrates a phenomenon tliat previously had been excluded from the literature. Tocqucvillc was following this strategy quite explicitly when lie did his research on the USA. Tocqueviile states: 'It is not, then, merely to satisfy a curiosity, however legitimate that 1 have examined America ... I confess than in America I saw more tliat America; I sought tliere the image of democracy itself, in order to learn wtial we have to fear or hope from its progress' (1946: 14).
TIie purpose of the extroverted case-study then becomes to explore futly this one case with the existing theory in mind, with the expectation of elaborating or expanding tliat body of theory with the resulting data.
Take, for example, Stein Rokkan's investigations of corporate pluralism in Norway (1966; sec Key Text 3.1 and also Olscn. 1987). These studies were being developed at. or even before, llic time in which there was a great deal ofthcorclk-al attention directed at the development of corporatism as a more general concept describing state-society interactions (Schmitter, 1974; 1989; VViarda, 1997). This work can also be seen as a reaction to the prevailing pluralist model of American political science. Indeed, one of Rok-k;m's most important arliclcs on tin; subject appears in a volume edited by Roben Dalil (1966), the leading figure in pluralist political science. The more genera! corporalist model implies a formalised and structured relationship between interest groups and the stale. The standard corporan.st model further implies a singular rclation.sllip between (lie state and each interest group, with government choosing a single group (or peak association) to represent each sector of the economy.

Key Text 3.1 Stein Rokkan and the Study of Centre-Periphery Politics
The Norwegian Stein Rokkan was one of the founders of contemporary comparative politics. He made a number of significant contributions lo the discipline, including developing the idea of 'corporate pluralism' (1966) that bridged the gap between corporatism and pluralism (see Key Text 2.2). He also developed some of the earliest concepts of data archives for the social sciences, and was instrumental in compiling such an archive at the University of Bergen.
One o( the most important of his contributions was the construction of a model derived from historical sociology to explain the development of centre-periphery politics in Western Europe (and see Lipset, 1967). This model argued that contemporary structures of political cleavage in Europe developed through successive overlays of three sources of cleavage- The first was the national revolution, as feudal decentralisation is threatened by centralising elites. The second was the Protestant reformation, and the continuing divisions between religions in countries such as Switzerland, Germany and especially Northern Ireland. Finally there was the industrial revolution with the separation between labour and capital that has been the dominant source of political conflict in European countries (or most of the twentieth century-Despite the significance of economic cleavages in Europe Rokkan pointed to continuing importance of the other sources of cleavage. This was to some extent a function of his observations of politics in Norway. with the political importance of peripheral groups such as fishermen and farmers. Further, he could not help but notice the importance of religious cleavages in other smalt democracies in Europe. Rokkan's background as a sociologist led him to emphasise these social bases of politics.
It might be argued thai Rokkan's theories were to some extent an attempt to generalise from Norway to the rest of Europe. Further, political. developments since the time of his book have pointed to some of the ways in which economic cleavages can be overcome in the management of stales. Still, Rokkan's contributions remain one of the foundations for the understanding of contemporary politics in Western Europe, and to some extent in the rest of the world.
The model developed hv Rokkan identifies a somewhat different relationship between state and society, in which llic state consults a wide variety of societal actors over policies, and expects them to bargain among themselves, as well as with the public sector actor or actors involved, until a consciTiiis is attained. This concept is similar to corporatism, in thai il requires [lie state to accord a legitimate

status lo interest groups, but diners in the number of groups involved and tlieir relationship among themselves- This fundamental observation and conceptualisation of' the nature of government in Norway was then expanded into a much longer treatment (Otsen, 1987). Corporate pluralism has also been the subject of critiques arguing that even if the model did succeed in building a theoretical basis for understanding politics in Norway, that model coutd not be extended to analyse other systems (Hcisler, 1979).
Tile second reason for using a single case is that tlie case may be the hardest one, so that if the theory appears to work in tills setting it should work in all otiiers. This strategy can be seen at work in many coniemporary analyses of Japan. The mystique of Japan as a distinctive political system lias grown to the point that it is being used as the most difncult test case for a variety of political theories, with the assumption that they will not work in that setting- For example, McCubbins and Noble (1995) undertook a study ofbudget-ary behaviour in Japan, testing the common assumption that this political system was dominated by bureaucracy and that there would be minimal political influence. Even in tliiscase, however, they found tliat there was a pronounced influence of political parties over budgetary choices, thus putting the usual characterisation of Japanese politics into question.
Finally, there is tlie 'Mount Everest' reason for doing studies with just a single case - it is there. That having been said, a careful and insightful examination of a single case, even one already very well known, may be proto-llieoretical. For example, it is not at all clear that Samuel Beer set out to develop general social science theory when lie wrote his second major study of British politics - Britain Against Itself (1982). That may not have been the intention, but his analysis of the blockages produced by the seemingly excessively pluralistic nature of British politics parallels closely Mancur Olson's more theoretical analysis of the Rise and Decline of ration', (1982), as well as some discussions of hyper-pluralism in the United States (see Peters, 1995b). In short, although it is not the usually recommended strategy for comparative research, an insightful analysis of a single country can produce large dividends, even if the benefits are unanticipated, or not even recognised, at the time.
Whether or nol ii is the bcsl strategy for llicory development for corn piir;t live politics, tlie single country study is likely to remain a cenlr;il feature of comparative politics fur a very long lime. Language and geographical restrictions are likely to persuade individual scho-

The Number of Cases 65
lars to focus ihcir attention on single cases, or at most a limited range
of cases. Furthermore, we might well think lhat, given llie continuing dearth of resources available for extensive multi-country research, there will be more rather than less attention paid to monographic studies of single countries. Tlie real task for comparativists, consequently, becomes to develop those individual case studies (sec below, pp. 139-54) so thai they have as much theoretical content as possible, while still retaining their descriptive richness. Tlie second part of that challenge is to work to compile the individual case studies into theoretically meaningful groupings and to attempt to draw some conclusions from them. (
Two, or a Few, Cases
We will now double the number of instances to be considered and think about llie logic of doing comparative analysis with only two cases. Using two cases appears to be a more sensible way to do comparative politics - then- is now something to compare. With properly selected 'focused comparisons' (Hague et al., 1992: 39-40) some comparative understanding can be generated from two cases. Despite that, this strategy is fraught with many of the same dangers encountered with single country analyses. Therefore, using two cases requires the same caution in design and execution as do single country studies. Indeed, the two country comparison may be even more dangerous, simply because it appears that a genuine comparison is being (lone, and then-lore llie logic of analysis must .surely be acceptable. Thai may 1101 be llie situation, however, and absence of care in ihe selection and analysis of the two cases may produce misleading results (De Winter el a!., 1996).
I'he problem with tilis mode ofanalysis is not smalt N per se, hut tlie mismatch between a rather small number of cases and a large number of variables (Lijphart, 1971: 686). When a country is selected for a comparative analysis, it brings with it a large bundle of variables. Tlie history, culture, economy and society all come along with the particular political dimensions in which the researcher is interested primarily. Therefore, lliere arc a liuge number of sources of extraneous variance, but only a few cases in which to aiicmpt to discover [he miinin;r in which all those variables operate. In statistical language, the dependent variable is over-determined, with too many possible fxpt.in.uions, so llial no real choice can lie made (Lupe-/.,

1993), Tlic researcher may focus on a few variables he or slie thinks are particularly importani, but unless the cases are selected carefully to falsify a hypothesis, any number of explanations will still be
acccptiiblc.
We must return to some of llie logic ofTeune and Przcworski in thinking aboul this form of comparison. Which two cases, and wliy? -these are the doniin.inl questions. In some instances, the logic of most dinercnt systems will direct us lo alicrnpt lo find two systems that are as different as possible on a number of variables, thereby maximising the variance with which to explore (lie differences among countries, The (rouble may be that with only the two cases llicre are so many variables that il is difficult to determine how to explain the diuer-ences. As Sartori (1991: 244) argues, (lie fundamental aspect of comparison is control, and the capacity to remove as many alternative explanations as possible from tlie 'equation', i.e. tlic implicit regression equation explaining the dependent variable.
Any two cases are in some ways comparable. Any two countries (or provinces, or whatever) that we select for analysis will have some features that arc comparable - they all have politics, they all have political institutions of some sort, they all make policies of some sort -but the question is whether the comparison is the best one for the particular item of research under consideration. The problem for comparison is tliat cases often are selected for reasons tliat are not scientific, but rather are based on familiarity, funding, convenience, or even commercial considerations (most two coumry studies seek to include the USA, given the size of the US market for books). If there is to be only a pair of cases then [liose cases should be as similar as possible on as many variables as possible, but (lie dominance of familiarity and convenience usually prevent dial from occurring.
One way to understand the logic of comparison for (wo cases is tliat this is itihcrcnttv a ^must different systems' design, and llie two cases must be conceptualised as almost totally different. Given tliaE a researcher lias no oilier information available when looking at the two cases, he 01" she must assume that tlic cases are substantially different. Tlic logic of comparative analysis, therefore, becomes to attempt to identify similarities between the cases (sec Chapter 2) that can then be used to explore common themes, rather than looking at their all-too-apparcm dilierences.
The dangers of binary research in compannive politics can be illustrated by Seymour Martin Lipsci's (1994) interesting, but

basically Hawed, example of (lie comparison of the United States and Japan as two 'exceptional' political economics. Tlic model lie uses is, in effect, a version of tlic Teunc and Prxewurski 'most diiTcrcnt system design'. The question Lipsct poses is, VVIi.il, if anything, can explain the economic success of these two very disparaic conn tries? Lipsel examines both on a variety of variables, and finds llicv differ fund amen tally on virtually all of tbeni, vet have both been vcrv successful. Fukuyama (1995) provides a more extensive examination of tlic economic success of systems, using some of tlic same variables used by Lipsel, but focusing on llie existence of trust in tlic c<Jmmcr-cial system rather than on the social and political variables that arc more central to Lipset's analysis. In particular, he points to the differences in the roots of economic success in Japan and Korea.
The research design flaw here is selecting cases on tlic dependent variable, combined with the extreme differences in llie systems, with the consequence that every difference appears equally invalid as an explanation. If, however, the cases had been selected with some variance on the dependent variable then liicre might have been some belter chance of generating more useful results. As we pointed out above, however, tlicre are disputes over the appropriatcness of selecting cases on the dependent variable, willi qualitative researchers arguing tliat tills is essential, and quantitative researchers arguing
tliat it invalidates most findings.
The problems with binary comparison can be reduced by focusing on a single institution, policy or process. For example, a researcher may want 10 compare the Britisli prime minister and the German chancellor (Helms, 1996). Given that these two oHiccs perform many of the same (unctions in government, some of tlie potential for extraneous variance is reduced- Further, because for most of recent history both of thesf ofnccs have been dominated by a single, conservative party, llie extraneous variance may be reduced further. These factors are still however no a guarantee that the research will make the contribution a scholar might like. Why these two countries? Is there anylliing theoretically interesting about (tie pairing of (wo cases, or have they been selected merely for convenience:* Roy Pierce (1995), for example, focuses on (lie presidency in France ;ind the USA as tlie two major examples of tills ollicc in developed democracies. as a me;ms ol understanding how electing llie chief executive ;tll'c( is voting, l)ui is slill able to make inieresUng tlieorcticsil arguments abuul tin- dillerences between tlie two sy.slems.

\ Smalt M Research in General
The same logic of comparability discussed above is applicable if researchers extend the analysis to a number of cases greater limn two, albeit still a small number. If 'the units arc very disparate, then (lie comparison in;iy have to be at such a high level of generality that the results are not very meaningful or useful for llieory development. Of course, (lie strategy of most different systems designs (pp. 37^H) argues for a great deal of diversity of cases, but that argument is more readily applicable to the tradition of statistical analysis rather than to the more constrained number of cases used for comparative analysis. With only a limited number of cases, the most different systems design usually generates comparisons of the type common when systems analysis and structural-functionalism were the dominant approaches to the comparative politics (Wiseman, 1966; Almond and Coleman, 1960; Jones, 1967). These functionalist studies managed to compare extremely disparate systems, but also managed to do so in such an equivocal manner that the results actually could say very little about what happened in those varied systems. In such a research outcome, there are simply too many factors that differentiate the systems to be
able to say what the more important independent variable or variables might be.
For a strictly comparative analysis, careful selection of cases is essential- Even then, it is not clear how much leverage [lie researcher can get for isolating cause and effect in the analysis. Lieberson (1991) argues that, for small J\' studies to be able to make causal claims, a number ol stringcnl conditions must be met, most of which simply do not exist in the social sciences. For example, he argues (pp. 309-12) that (he cause must be deterministic rather than probabilistic. That is, for a study with only a Few cases, to say tliat A' causes ?, the linkage must be necessary and sufficient, and }" will not occur without X. Very few relationships in political science would meet that criterion, and even more 'advanced' social sciences depend heavily upon the cetens fxinbus disclaimer. Most of the relationships with whidi we work are probabilistic, and with a small sample it is not possible to rule out a chance finding.
Furllier, Lieberson also argues that for small-A" studies lo demonstrate causaiion, llierc c;in only tie a single cause, and no interaction among independent variables. This statement assumes that [he mcihods for determining causation developed by Mill (see above, pp. 29 30) are being applied, but llie ;irgumcni would liold even

without that assumption. With a small number of cases there are rarely sufficient cases to have all possible combinations of several independent variables, so that the research runs the risk of falsely imputing causation when changes in the dependent variable may well be a function of interactions among variables. Given the complexity of most social processes, those interactions are almost inevitable. Lieberson also argues that for these mctliods to work there must be no measurement errors. In other words, for small-JV" studies to produce valid causal results, [here is no room for either extraneous or error variance, both of which are almost unavoidable in tlic social sciences.
There have been several critiques of the rather rigid claims made by Lieberson. For example, Savolainen (1994) argues that Lieberson has confused comparative methods used to prove causal assumptions with those intended to eliminate possible causes. Establishing that X causes }" is difficult; it is much easier to argue that X does not cause Y (see also Skocpol, 1984). Eliminating possible causes is in itself a valuable service to comparative politics, however, given the number of contending theories of cause available. Similarly, Savolainen argues that probabilistic explanations can be used with small-jV studies, assuming that the researcher is conservative in the claims made for the findings- The same would be true for the presence of interaction effects in the explanation. Even if we grant [he critics their points, imputing causality with a small A is difficult, however carefully [he cases are selected in advance. Tlie complexity of the social and political world is such that eliminating other possible causes is difficult. The Boolean approach (sec below, pp. 162-73) begins to address these problems, lint the findings then still depend upon the nature and size of the sample used.
Tims, very much like the single country case studies, small JV studies appear more useful for generating hypotheses than for testing them. The only viable exception to tilis statement appears to be in carefully crafied, most similar systems designs, wlien [lie similarity of the countries selected can be demonstrated very clearly and convincingly. Without that knowledge of die countries, llie capacity of small-A studies for making statements about causation appears a very limited indeed. Even in 'comparable' cases, however, Prxeworski and Tcune (1970) would argue lhal llie dependent variable would most likely Ix- ovcr-dclcrmim'd because of the number ol" rival hypotheses [lial could nol be rejected on (lie basis of any small mimbcr of cases.

Reducing Variables
An alternative method for coping with (lie small-X, many variables* problem is to reduce tlic number of variables included in the ;in;itysis (Collier, 1993). This reduction can be done ill one of two manners. Tlic first way is to employ a more elegant theory, with lower presumed explanatory variables tti;>ii oilier contending approaches-The argument here is that if the researcher goes into the lield with a loosely constructed theory, then the data from ;t small number of cases can support any number of possible theoretical explanations. If, on the other hand, the researcher works witli a clearer and more parsimonious theorv, then that theory can be tested with the limited number of cases. This is especially true if (lie cases are selected to make Falsification more likely, for example, if the researcher looks (or llie hardest cases. Collier, for instance, uses (he example of rational choice theory, with a very few variables and relatively simple hypotheses.
The danger of the variable reduction strategy is that the researcher imposes a premature closure on the possible explanations for the phenomenon. Just because a single hypothesis can be tested witli a limited number of cases does not mean that there are not otiicr possible explanations. Further, a strong theory such as rational choice may contain a number of untested assumptions that arc, in many ways, also hypotheses. Failure to test tlic assumptions empirically may lead (tie researcher to accept twhat is in essence a spurious relationship. For example, in the case used an example by Collier (Geddes, 1991), a game theoretic analysis was applied to explain administrative reforms in Latin America. This appears to be an elegant treatment of those reforms witli few variables, bin also appears lo avoid a number of factors lliai scholars coming from other traditions might consider crucial components of any investigation of administrative reforms. Most scholars of public administration, for CNample, might consider the exclusive focus on legislative decision-making for studying administration risible.
The alternative means of reducing the number of variables is to perform that task empirically rather tlian theoretically. Many "fthe variables that researchers use in comparative research are closely allied to oilier variables, so that not only arc tliere statistical problems In using them together, l)ul lliere may also lie conceptual and tlicorrlical confusion. The statistical problem i** iniilluolliiic.irny. or the confounding cdi-cis of highly iiitemirrelaird independent vari-

ables in regrcsaipn equations. This tends both to reduce the reliability oCthe estimates and also to reverse signs for the variables that are not the mostly strongly correlated with the dependent variable. The
theoretical problems arc more dillicult to solve.
A variety "1 statistical techniques such as factor analysis can be used to combine possible independent variables, and, even without these statistical techniques, indexes can be created to combine variables that are conceptually related. These aggregation strategies do not permit tlic researcher to answer questions about tlic relative cnccts of (lie ctoscly related components of llicsc 'syndromes' of variables, but they do permit tlic testing of theories in rather broad ways, with the possibility of later refinements of the analysis witli the
individual variables.
For example, a number of micro-level comparative research projects have used various data aggregation techniques to produce more parsimonious explanations. The typical method is to collapse a number of separate independent variables into composite explanations using methods such as factor analysis (Lewis-Beck, 1994). These aggregation techniques select a number of candidate independent variables, and identify underlying dimensions that link those variables. Thus, one variable can be used to represent a number. Further, these techniques produce dimensions lliat are themselves uncorre-laled, so eliminating any further statistical difficulties.
One potential pitfall in doing small-./V research is to select cases on ihe basis of values of the dependent variable rather than on those of the independent variables. This is an all too human tendency. Researchers identify several cases that are interesting because of their success or failure, and then proceed to study them alone, for example, cases of successful democratisauon. Tlic problem is that even if there arc independent variables that arc highly correlated with those dependent variables, there is no real variance to explain. How do we know tliat the same pattern would not emerge for cases tliat were unsuccessful, or that did not attempt to democratise at all?
Research based on a common value of the dependent 'variable' can eHcctively eliminate viable hypotheses - if none of llie cases in the sample exhibit a certain trait [lien it is rallicr certain that this variable is not a concomitant of thai dependent variable. This statement again ]X)inis to tlic essential role of theory in tlic selection and analysis of comparative cases, anci in guiding tlic collection of data. If we do not initiate research with some ihcorclic.il i^iifl.mcc then we will not know winch hypolhe.sfs in consider aiii-l which to

reject. Further, withoul (lie theory we will not even recognise what data to look for lo be able to reject relevant hypotheses. There is no shortage of interesting research questions, but the real consideration is how to relate those specific questions to more genera! theories.
Courtier/actuals
If nature supplies the researcher with too few usable cases, or if funding agencies supply the researcher with too tittle money to investigate .ill the potentially usable cases, there may still be a way to increase the A of the study, and thus satisfy the usual scientific canons. One of the more interesting ways is to develop counterfactual arguments that are, in effect, additional cases. Max Weber (1949; see also Polsby, 1982) actually discussed this as one strategy for dealing willi the problem of too few relevant cases for many issues in social research. Fearon (1990) also has argued for using this methodology for comparative research, and its logic lias been examined relatively thoroughly in several recent methodological studies (Tetlock and Belkin, 1996; Kahneman, 1995). Fearon argues that this style of analysis is at least a partial antidote to the research problem already mentioned several times - having a collection of cases without variance on the dependent variable. With counterfactuals, researchers can always generate such variance, even if it does not occur in the 'real' world.
Arguably, any small-A" study is based on counterfactual arguments. If causation is imputed to a cause in the case-study, or in a study with only a few cases, tlie assumption is that were there cases lliat had the other values on a variable present then the outcomes would have been different. A case researcher tells a causal story, and must attempt thereby to dismiss other causes and to show that liad things bcc-n different then the outcome would have been different. In [lie example tfiai Fcaron uses, Alfred Stepan (1988) argues why a military coup in Brazil was not inevitable but, given particular events and decisions by [he government, did eventually occur. In the criteria for counterfaclual arguments advanced by Tetlock and Belkin (1996:
19-22), one of tlic guiding principles is that arguments that require fewer deviations from the 'real world' and the specification of fewer
steps are more realistic than more elaborate departures from observations.
Przcworski (1995) argues ihilt counierlactual argument is essential
to comparative political aii.tly.sis. The limited number of cases *

The Number of Cases 73
available for any interesting research questions means that the researcher inevitably must use counterfactuats, especially to fill in the cases that are more extreme. Nature rarely provides the researcher with llie full range of cases that might he needed to test some hypotheses, so that tlie only option is to ask 'What if . . .?', and attempt to fill in [hose missing cases in as unbiased a manner as possible. These 'thought experiments' are not substitutes for field research, in Przeworski's view, but they are crucial (or developing theories after the range of real, available cases has been exhausted.
Analogies
It is also easy to move from 'what if to 'as iP. That is, analogies can be an important source of comparative case material and counterfactuals. The use of analogies lias been developed more in the study of international relations than in comparative politics, but the logical basis of their use is very much llie same in the two fields. Khong (1992; see also Houghton, 1996), for example, examined the extent to which various analogies were used tojustify decisions in foreign policy debates, and tlic extent to which the analogies selected could explain decisions. One way to employ analogical reasoning for comparative politics is to think about time more creatively and to utilise historical cases that are functional analogies of more contemporary events (see Bartolini, 1993: 139ff.). This style of analysis may be especially important for studying political development as countries today go through processes that are not dissimilar from processes that others went through decades ago.
For example, Halpcrin (1997) discusses asynchronic comparisons of weak slates in contemporary mid-East and medieval Europe. The logic of this analysis is clear. In cadi case, there were states thai, by contfinporary standards, were wcak'and liad diulcully in enforcing their authority throughout their territory and dominated by informal politics. By using (lie two sets of countries, the researcher had increased her A' significantly. If tlic processes in tlie two sets of systems appear similar, despite their separation in time and space, then there is greater hope that a general explanation of development can resull from the analysis. This strategy of asynchronous comparison appears potentially extremely fruitful, but also raises questions, iriosi notably just what sort of evidence would be needed to c-siablisb tlic functional equivalence ofdillercnt eras and political CVCIHS- "I'lierc appear ID be no clear i-uk"i yet for this strategy, the tcsl being what

survives when it is exposed to ttif scrutiny of llic remainder of the scholarly community.
In summary, the countcrfactu.il siraicgy of coping with confirmation of hypotheses is the .mtithcsi'i of the statistical method (see below), Fcaron argues that this strategy is to be preferred in many ways, because i[ docs not give ihc researcher a false sense of security. Tlic largc-A slucly assumes iliiit all the threats to validity arc taken care of by the size of the sample, but in social science tliat may not be the case. Thai assumption mav be especially problematic in comparative politics, given the lack of independence of tlif units of measurement and the problems of diffusion and compensatory cnects in the dependent variable. There may well be a number of systematic retail onships and a systematic dispersion of political practice, which make the independence of observations very suspect.
Comparisons of'Natural Groups'
Another strategy for comparison is to begin with relatively small groups for comparison, with those groups being defined as composed of relatively homogeneous 'families ol nations' (Castles, 1993; Esping-Andcrson, 1990 - see Key Text 10.1). For example, there lias been a great deal of interesting and useful research done comparing the Scandinavian countries (Elder el a/., 1988; Lundquist and Stahlberg, 1983; Laegreid and Pedcrsen, 1994). These countries (three to live, depending upon how one counts) have a number of political, economic and social characteristics in common. Further, they countries arc in almost constant contaci witli one another on issues of policy and administration, so tin" researcher can determine relatively clearly how ideas liliered through national political settings can be implemented. Thus, while this research may liave tlie advantage of liolding constant a number of socio-economic and even political factors, it has (lie disadvantage of a severe case of Gallon's problem, that is, sorting oui tlic eni'cls ofditl'usion from (lie effects of indigenous developments (see pp. 41-3).
Anotlicr of these natural groups of countries for comparative analysis is the 'Old Commonwealth', or the Westminster democracies, meaning those industrialised democracies derivative of the-British tradition, including Britain, ;ind sometimes tin' United .Slates to make the 'Angle American democr.icies' (Lijphari, 1984; 1990;
we also Aucoin/ 199.'"). ll is a.ssunn'd that llii-s ci"nnmKi heritage

makes these countries readily 'comparable'. Ycl, if we look at some relevant data on this group of countries (Tables 2.1 and 2.2), we find that in many ways they are quilc i i etc rogen ecus socially, economically and politically. Therefore, any comparison among these countries lends to be arguing implicitly that political heritage and political culture are more important features than arc the social and economic fabric of a country. Further, it lends to he arguing that for comparison the constitutional heritage is more significant than even some important structural features of constitutions such as federalism.
That argument would be particularly interesting were llic comparison extended to cover the members of the 'New Coinmomnwcalth' (see Hraibanti, 1966). In these countries, there was also a long period of British rule, and a direct implementation of British governmental institutions before and after independence. Thai connection was substantially longer in some cases (India, Pakistan) than it was in tlic United Slates, and more recent than in most of (he Old Commonwealth countries. The failure to include llicse countries in most comparative analyses looking at tlic impact oF the Westminster model therefore seems to argue that cultural and social factors arc more important than constitutional inheritance. So lliese two implicit arguments are inconsistent, but the contradiction does point to the way in which conventions and indeed prejudices can creep into comparative analysis-
Allhough the comparison of these families of nations may face some apparent or not so apparent problems, there are also some potential benefits. Joseph LaPaIombara (1968), for example, argued in favour of developing 'middle-range theories' of comparative politics, rather than tlie grand theories such as .systems analysis or siructural-lunclionalisin that tended to dominate comparative analysis when LaPaIombara was most concerned with theory development. These middle-range theories would address the politics of a geographical region, or perhaps a government institution, ralhcr than providing the global explanations sometimes thought necessary to qualify as a theory. By using this mid-range strategy, LaPaIombara argued, the discipline could develop building blocks for tlic more comprehensive theories while at the same lime providing more useful and convincing explanations for politics within (hose more limited domains. Roy Macricii.s (1986; 22) supported lli.it view, and argued that 'clustering [geographically], a.s opposed to (lie search for grand ihcory, has g^vcn to tlie field a new vitalilv, and may ultimately pave tlie way to llic development of some unifying models and priorities'. We will point out (sec Chapter 5) some problems in defining the clusters, but this docs appear to be tlie current direction ol' theory development.
Sometimes, without explicitly acknowledging the strategy, comparative politics has been proceeding in this direction. Any number of books and articles have been published ofTering theories for some parts of the world, or for particular institutions. Take for example, Hyden and Bratton's (1992) work on governance in Africa. The theoretical chapters of this book address primarily questions of African politics and the breakdown of governance in that continent, but the general considerations about governance raised there could be applied anywhere. Thus, by developing a theory about governance in Africa, the authors have actually made a good beginning on a
more genera) theory about governing, and especially about governing in less-developed political systems.
One subsidiary question that arises is how to determine the appropriate focus for these middle-range theories. As pointed out above, the natural groups that we might begin with do not always have the degree of homogeneity assumed. Although Hyden and Rratton's analysis of African states is interesting, the degree of variance in political form, political tradition, social structure and the like among those nearly fifty sub-Saharan states may make attempting to piece together one approach to fit them virtually liopeiess. Indeed, such an approach may have to be so general that it would become capable of being applied almost anywhere, regardless of (lie geograpliical location. On the oilier hand, schemes that have been put forth as theories of European politics tend to do belter
at describing and explaining a part of Europe rather llian the diverse politics in that continent.
One approacli to die problem of identifying an appropriate focus for a middle-range theory is to make that determination empirically. As discussed above, some approaches to comparative politics (perhaps more appropriately referred to as statistical analyses of sets of countries) have employed factor analysis and other dimensional techniques to identify meaningful clusters of countries (Rummcl, 1972; Casiies and Mitchell, 1993; Peters, 1993). This body of research has tlie virtue of being able to demonstrate that (lie countries in question do constilute a statistically meaningful group, but is potentially suspect on other ground;). In particular, the clusters of countries tlial emerge arc a function ofihc data ilia! are put into the clustering programme. Iftin-'re was inadfqu.ne theory guiding selection of the concepts, or even inadequate measurement of (lie concepts used, then

the results wilt not necessarily reflect the groupings of countries that actually exist.
Further, having grouped countries in this way, it may be difficult to employ the groupings to test comparative propositions anyhow other than through tlie most similar systems design. If anything further is done witli tlie data within a grouping, the results may be almost predetermined. As Teune (1990: 43-4) points out, 'Selecting a type to reduce variance made it impossible to find out what diiTerence the category of inclusion made. Thus, if being wealthy and democratic has consequences, it is necessary to look al some cases of being non-democratic and poor.' What therefore may be most interesting approach to comparison is a two-stage process. At the first stage, some dimensional technique can be used to identify groups of countries, while in the second stage comparisons are made across the groups, rallier than within tlicm. This strategy does not meet all the stipulations of LaPalombara's mid-range theories, but it does enable the creation of theories that dinerenliate among groups of
cases.
Global Comparisons
Finally, we come to what might be considered to be the dream of the statistical version of comparative analysis - global comparisons of virtually all political systems. We have noted already that there have been several major research studies of this type, attempting to develop measures and concepts that would travel, and then to classify the countries of tlie world on those variables. In many ways, these global studies represented tlie early, euphoric days of the behavioural revolution in political science theory and tlie computer revolution in the managing ofdata. The assumption was that if we could just get enough data from enough political systems then we could answer all the relevant questions of political science.
fhe euphoria concerning this style of research quickly wore ofT, and lias been replaced witli some healthy scepticism. First, as we point out below in Chapter 4 on measurement, developing measures that can travel from (lie United Kingdom to South Korea to Vanutu often implies that they become so general that they mean very little, and actually are able to contribute very little in (lie development of social science theory. For example, jean Blondel's study (1990) of political leaders and institutions around the world lias been criticised for iis generality and its failure to make useful interpretative stale-

ments (sec also Key Text G.2). For Blonciel, there were so Few indicators that could 'travel' across ihis range of systems that [here was rclalivcly little that could be .said to compare the systems, despite the importance simply or amassing comparative information on political executives that was not previously available.
Similarly, the idea of the country as ;i unit of analysis and as a meaningful entity tends to become lost in studies of this nature. A country simply becomes a data point, and (lie possibilities of understanding why and how Vanutu or Bulgaria functions the way it does may be sacrificed on a statistical attar. This research may be comprehensive statistical analysis, but often it is not really comparative politics. Comparative politics is constantly forced to trade off the particular for the general. Individual scholars must decide if they are experts in one country, or even one region of one country, or in one region of the world, or in comparative political theory that spans the globe - it is dinicult to do all those things- Also, we must decide whether the real questions to be answered are about real countries or about distributions of data.
Summary and Conclusion
Comparative politics requires the selection of particular cases in the pursuit of genera! theory. At the extreme, a wide range of cases should be used, but that is a luxury available only for aggregate data analysis or a few extremely well-funded studies. Further, involving a large number of cases may mean that cadi one is not addressed carefully. If there is to be any primary data collection tlicn there must be some selection of cases, and witli tliat (tie development of criteria for how many arc sullicient. This chapter should have demonstrated that ttierc is no single answer to questions about [lie appropriate size or composition of samples for comparative research.
What is crucial in this discussion is lliat the size and nature of the sample be determined by the questions tliat are being addressed, rather than some predetermined idea of how research should lie done-In some instances a single case is all that is required, and indeed in some instances more tii;"n one case might nniddy the water rattier than clarify the issues aJ hand. If a single c.isc is selected wisely, and the research is done thoroughly, it may say a good deal more than any statistical s[iid\. On the oilier h;ui<l, there arc some questions that may rc<[uire a large sample and rail for including as many cases ;is possible.

This chapter has pointed out that an iniermediate strategy is often a good option for comparative research. Developing approaches that capture some of the complexity of individual c.iscs in a geographical reeil*", but still pel-mil covering some portion of the possible cases, mav provide something approaching the best of both worlds. Despite its potential virtues, however, this approach can be taken too far. It can produce research that takes as given what may be important hypotheses, for example, tliat the countries within the regional classification arc similar in theoretically relevant ways. Fiii-tbcr, this strategy can virtually eliminate the testing of some hypotheses by limiting the range of variance available. Like almost everything else about comparative politics that we have discussed here there is a traclc-olf, and there is no magic solution to substitute for the good judgment of the scholar in making decisions.

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