Erik W De Kwaadsteniet
email: kwaadsteniet@fsw.leidenuniv.nl

Eric Van Dijk

Arjaan Wit

David De Cremer

'How Many of Us Are There?': Group Size Uncertainty and Social Value Orientations in Common Resource Dilemmas

Keywords: group size uncertainty, social dilemmas, social value orientations, tacit coordination

In two studies, we investigate the effects of group size (un)certainty and social value orientations in common resource dilemmas. By focusing on this largely unexplored type of environmental uncertainty, we show that, in contrast to the often replicated fi nding that resource size uncertainty leads to over-harvesting in common resource dilemmas, group size uncertainty is not necessarily detrimental to the collective interest. Furthermore, we argue and show that whereas under group size certainty people base their individual harvests on the equal division rule, under group size uncertainty they base their harvests on their own social value orientations: whereas under group size certainty both proselfs and pro-socials harvest about an equal share of the common resource, under uncertainty prosocials show self-restraint in order to further their group's outcomes.

A well-known type of social dilemma is the common resource dilemma (or commons dilemma). In this type of social dilemma, a group of people have access to a limited common resource. A real-life example of such a resource dilemma Social dilemmas are situations in which people face a confl ict between their personal interests (called defection) and the interests of their group (called cooperation). In such dilemmas, people thus have to choose whether to defect or to cooperate. A choice to defect yields the best payoff to individual group members (i.e. in at least one of the possible outcome confi gurations; [START_REF] Liebrand | Social dilemmas: Individual, collective, and dynamic perspectives[END_REF], whereas all individual group members are better off if all cooperate than if all defect (see [START_REF] Komorita | Interpersonal relations: Mixed-motive interaction[END_REF]Kopelman, Weber, & Messick, 2002, for reviews).

is the environmental problem of over-fi shing. In this resource dilemma, a group of fi shermen have access to a natural common resource, namely the fi sh population. When individual fi shermen choose to further their self-interest by catching as much fi sh as they can, the collective interest is jeopardized because excessive fi shing increases the chance of the resource becoming depleted. So whereas individual fi shermen may be tempted to overuse the common resource, the collective interest calls for moderate use. Moreover, to further complicate matters, fi shermen often do not know how large the fi sh population is or how many fi shermen are fi shing from the same pool [START_REF] Ostrom | Governing the commons: The evolution of institutions for collective action[END_REF][START_REF] Takigawa | Group size uncertainty in shared resource use[END_REF].

Many real-life social dilemmas are thus characterized by environmental uncertainty, or uncertainty regarding the characteristics of the task environment of a social dilemma [START_REF] Messick | Framing and communication effects on group members' responses to environmental and social uncertainty[END_REF]. Earlier research has shown that environmental uncertainty can have a large impact on people's choice behavior. For instance, earlier studies have repeatedly shown that uncertainty regarding the size of the resource (i.e. resource size uncertainty) leads to over-harvesting (e.g. [START_REF] Budescu | Resource dilemmas with environmental uncertainty and asymmetric players[END_REF][START_REF] De Kwaadsteniet | Social dilemmas as strong versus weak situations: Social value orientations and tacit coordination under resource size uncertainty[END_REF][START_REF] Gustafsson | Over-harvesting of resources of unknown size[END_REF][START_REF] Hine | Individual restraint and group effi ciency in commons dilemmas: The effects of two types of environmental uncertainty[END_REF]; see [START_REF] Van Dijk | What we know (and do not know) about the effects of uncertainty on behavior in social dilemmas[END_REF], for an overview of the effects of uncertainty). However, until now very little experimental research has been done to investigate other types of environmental uncertainty, such as uncertainty about the number of group members sharing a resource (see [START_REF] Au | Effects of group size uncertainty and protocol of play in a common pool resource dilemma[END_REF], for an exception).

In real life, group sizes are often uncertain. In many social dilemma situations, people do not know precisely how many group members there are. For instance, water consumers often do not know how many people are consuming water in their water district (see [START_REF] Ostrom | Governing the commons: The evolution of institutions for collective action[END_REF][START_REF] Takigawa | Group size uncertainty in shared resource use[END_REF], for numerous other real-life examples). Therefore, more experimental research is needed to obtain more insight into this type of environmental uncertainty [START_REF] Van Dijk | What we know (and do not know) about the effects of uncertainty on behavior in social dilemmas[END_REF]. In the present research, we will investigate how group size uncertainty infl uences choice behavior in common resource dilemmas.

Earlier research on group size uncertainty

To our knowledge, only one experimental study has been conducted to investigate group size uncertainty in social dilemmas. In an earlier paper in this journal, [START_REF] Au | Effects of group size uncertainty and protocol of play in a common pool resource dilemma[END_REF] investigated the effects of group size uncertainty in a single choice step-level common resource dilemma under different protocols of play. Each of their participants made only one harvesting decision in a series of successive rounds, either in a pre-specifi ed order (called a sequential protocol) or whenever (s)he decided to do so (called a selfpaced protocol). Overuse of the common resource would destroy its value and none of the harvests would be granted. In the group size certainty condition, participants were told that the group size was five. In the group size uncertainty condition, they were told that their group was equally likely to be any size between three and seven persons. In all conditions, after the fi rst round participants were fully informed about the combined harvests of all the preceding players in the sequence, but in the self-paced protocol participants were also informed about the number of players who had made requests in the previous round.

The authors were primarily interested in effects on total requests, i.e. effects at the collective level. Their analyses showed that collective overuse was less likely to occur under group size uncertainty than under group size certainty. Under group size uncertainty, participants apparently acted as if the group size was large and requested less, to avoid collective overuse. Ancillary analyses showed that in the self-paced protocol of play, group size uncertainty resulted in participants delaying their harvest decision to a later round until they knew the combined harvests of all the preceding players in the sequence, reducing the risk of collective overuse. By contrast, participants who were certain that the group size was fi ve did not wait and were more likely to make a request in the fi rst round. Given that they-on average-requested somewhat more than their equal share (i.e. 1/5th of the common resource) the pool was more likely to be overused under group size certainty than under group size uncertainty. It may be suggested that the self-paced protocol allowed participants to coordinate their actions. Under group size uncertainty, a participant could gain useful information about the number and the (combined) size of others' requests by delaying his or her own harvest decision to a later round. This raises the question as to what will happen if uncertainty about the number and size of others' requests cannot be reduced by strategic timing of one's decisions.

To investigate the effects of group size uncertainty without the possibility of the strategic timing of decisions, the present studies use a simultaneous protocol of play, in which participants will not be informed about the harvests of their fellow group members. By doing so, we can obtain more insight into the inhibiting effects of group size uncertainty on tacit coordination.

Moreover, to answer the question as to how people make decisions when the possibility for tacit coordination is limited, we draw on [START_REF] Snyder | Personality and social behavior[END_REF] framework of strong versus weak situations. On the basis of this conceptual framework, we will argue and demonstrate that under group size uncertainty people base their harvesting decisions on their own social value orientations.

Tacit coordination and group size uncertainty as a weak situation

In social dilemmas such as the one described above, it is important for people to coordinate their choice behavior effi ciently (e.g. Van Dijk & De Cremer, 2006;[START_REF] Van Dijk | Tacit coordination and fairness judgments in social dilemmas[END_REF]. In resource dilemmas, it is best for people to coordinate their decisions in such a way that the collective resource does not become depleted, which would be detrimental to individual as well as collective interests. However, effi cient coordination is hampered when group members do not know what their fellow group members will decide. This uncertainty about the decisions of other group members is called social uncertainty (or strategic uncertainty; [START_REF] Messick | Framing and communication effects on group members' responses to environmental and social uncertainty[END_REF]. Earlier research has shown that people can often deal with such social uncertainty by means of tacit coordination [START_REF] Schelling | The strategy of confl ict, 1980 edition[END_REF][START_REF] Van Dijk | Tacit coordination and fairness judgments in social dilemmas[END_REF]. That is, group members can predict their fellow group members' decisions by using so-called tacit coordination rules (such as the equal division rule; see also [START_REF] Allison | Social decision heuristics in the use of shared resources[END_REF]. Furthermore, people also use such coordination rules to determine their own choice behavior.

Imagine a resource dilemma with the same payoff structure as the one Au and Ngai used (2003). In this type of dilemma, a group of fi ve people own a collective resource of 500 coins. Each individual group member can request a number of coins from this resource. However, if the total group request exceeds the number of coins available in the collective resource, the resource becomes depleted and no one receives any coins. The fi ve group members cannot communicate with one another and do not know what their fellow group members will decide (i.e. social uncertainty). Research has shown that people tend to solve this social dilemma by using a tacit coordination rule, in this case the equal division rule. In other words, most group members will request an equal share from the collective resource (e.g. [START_REF] Allison | Social decision heuristics in the use of shared resources[END_REF], in this case 100 coins. If all group members decide to do so the resource is optimally used and all group members receive 100 coins. Thus, under certainty in a resource dilemma, people can tacitly coordinate their decisions by applying the equal division rule.

In order to apply the equal division rule, however, people need specifi c and accurate information about the task environment. To calculate an equal share people have to divide the size of the collective resource by the number of group members. In order to do so, they need to know exactly how large the resource is and how many people the group consists of. Thus, when the group size is uncertain it becomes much more diffi cult for group members to apply the equal division rule. What do people base their decisions on under such group size uncertainty?

The answer to this question may be found in Snyder and Ickes' framework of weak versus strong situations (1985; see also [START_REF] Roch | Effects of environmental uncertainty and social value orientation in resource dilemmas[END_REF][START_REF] Van Lange | Movement in social orientations: A commentary on Kelley[END_REF]. Snyder and Ickes distinguish two types of situations. Strong situations are situations that provide salient cues for people to base their decisions on. In strong situations, people base their decisions on these salient environmental cues. As a result, strong situations lead to little interpersonal variation in their decisions. Weak situations, by contrast, do not provide people with such salient environmental cues. In weak situations, people cannot use external cues to base their decisions on, but they base their decisions on their own dispositional preferences.

When we apply this framework to group size (un)certainty in social dilemmas, we can characterize social dilemmas with group size certainty as strong situations. After all, under group size certainty most people may decide to base their choice behavior on the equal division rule. By contrast, social dilemmas with group size uncertainty can be characterized as weak situations that do not provide people with the salient cues to apply the equal division rule. Under group size uncertainty we can therefore expect people to base their decisions on their own dispositional preference for either cooperation or non-cooperation, i.e. their social value orientation.

Social value orientation (SVO) is a personality variable that indicates how people evaluate outcomes for themselves and others [START_REF] Messick | Motivational bases of choice in experimental games[END_REF][START_REF] Van Lange | Social value orientation and intelligence: A test of the Goal Prescribes Rationality Principle[END_REF]. Generally, a distinction is made between three types of SVOs (e.g. Van Lange, 1999): (a) cooperation, i.e. the preference to maximize joint outcomes and establish an equal distribution, (b) individualism, i.e. the preference to maximize own outcomes, and (c) competition, i.e. the preference to maximize the relative advantage of own outcomes. Cooperators are commonly referred to as prosocials, and individualists and competitors as proselfs. In social dilemmas, prosocials generally show more cooperative behavior than proselfs (e.g. [START_REF] Kramer | Social values and cooperative response to a simulated resource conservation crisis[END_REF][START_REF] Liebrand | The effects of social motives on behavior in social dilemmas in two cultures[END_REF].

Study 1

Based on the above, we predict an interaction between group size uncertainty and SVO on individual requests. Under group size certainty (i.e. a strong situation), we expect that proselfs as well as prosocials will base their harvesting decisions on the equal division rule and therefore we predict a limited difference between proselfs' and prosocials' individual requests (Hypothesis 1). Under group size uncertainty (i.e. a weak situation), by contrast, we expect that participants will base their decisions on their own SVO, and therefore we predict a (signifi cant) difference between the individual requests of proselfs versus prosocials, i.e. prosocials' requests being lower than those of proselfs (Hypothesis 2).

Method

Participants and design Participants were 120 students at Leiden University (15 men and 105 women, mean age = 20.80 years) who volunteered for the study. At the beginning of the experiment each participant's SVO was assessed. Group size uncertainty was manipulated as a within-subjects factor. Accordingly, a 2 (SVO: Proselfs vs. Prosocials) × 2 (Group Size Uncertainty: No vs. Yes) factorial design with repeated measures on the latter factor was used.

Procedure The participants were invited to participate in a study on 'group decision making'. Upon arrival at the laboratory they were seated in separate cubicles, each containing a personal computer. This computer was used to give instructions to the participants and to register the dependent measures.

Assessment of SVO At the beginning of the experimental session, participants completed the nine-item version of the decomposed games measure to assess their SVOs [START_REF] Van Lange | Development of prosocial, individualistic, and competitive orientations: Theory and preliminary evidence[END_REF]. The decomposed games measure has excellent psychometric qualities. It is internally consistent (e.g. [START_REF] Parks | The predictive ability of social values in resource dilemmas and public good games[END_REF], reliable over substantial time periods [START_REF] Eisenberger | Effects of social values, effort training, and goal structure on task persistence[END_REF], and not related to measures of social desirability (e.g. [START_REF] Platow | An evaluation of the social desirability of prosocial self-other allocation choices[END_REF]. The task consists of nine items, each containing three alternative outcome distributions with points for oneself and an anonymous other. For each of these nine items the participants had to choose which of the three distributions they preferred. Each item contained a prosocial (e.g. self: 500, other: 500), an individualistic (e.g. self: 560, other: 300), and a competitive option (e.g. self: 490, other: 90).

Participants were classifi ed as prosocial, individualistic, or competitive when at least six out of nine choices were consistent with one of these three orientations (e.g. [START_REF] Van Lange | Social value orientations and impressions of partner's honesty and intelligence: A test of the might versus morality effect[END_REF]. Out of 120 participants, 54 (45%) were classifi ed as prosocials, 40 (33%) as individualists, and 12 (10%) as competitors. Fourteen participants (12%) could not be classifi ed and were therefore excluded from further analyses. As in many earlier studies (e.g. [START_REF] Kramer | Social values and cooperative response to a simulated resource conservation crisis[END_REF][START_REF] Mcclintock | Role of interdependence structure, individual value orientation, and another's strategy in social decision making: A transformational analysis[END_REF][START_REF] Van Lange | Social value orientations and impressions of partner's honesty and intelligence: A test of the might versus morality effect[END_REF], individualists and competitors were combined to form one group of proselfs (n = 52; 43%). After completing the SVO measure, participants responded to some fi ller questionnaires. Next, they were presented with the resource dilemma.

The resource dilemma Participants were informed that they would be part of a group of people, that each group member was sitting in a separate cubicle and that there was no communication possible among participants. Furthermore, participants were not aware of the identity of their fellow group members. Decisions had to be made privately and anonymously.

The participants were presented with two similar resource dilemmas that only differed in the degree of group size uncertainty. Participants learned that at the end of the experimental session a computer would randomly select one of these two situations and that this selected situation would be used to calculate the amount of money each individual group member would earn. Since only the selected situation was used to calculate the participants' earnings, each of these two situations can be considered an independent single-trial resource dilemma.

In each of these resource dilemmas, each group member could request any number of coins from a collective resource of 500 coins. Each coin was worth 0.01 euro (1 euro was approximately US$1.35). For each of these resource dilemmas it held that if the group's collective request would be smaller than or equal to the resource size, the requests were granted and each group member would earn the amount of money he or she had requested in that situation. However, if the group's collective request exceeded the resource size all group members would earn zero outcomes. This resource dilemma is similar to the one used by [START_REF] Au | Effects of group size uncertainty and protocol of play in a common pool resource dilemma[END_REF] but in the present study participants had to make their decisions simultaneously. Moreover, during and between the two resource dilemmas no feedback was given about the decisions of the other group members nor about the group's collective request.

Manipulation of group size uncertainty

The two situations only differed in the degree of uncertainty about the size of the group. Group size uncertainty was manipulated by varying the range of the uniform distribution of the group size. The midpoint of these ranges was kept constant across the two conditions, namely fi ve. Under No Uncertainty, the group size was certain, namely fi ve group members (midpoint = 5, range = 0). Under Uncertainty, the group would consist of at least two and at most eight group members (midpoint = 5, range = 6). Participants learned that the exact size of the group in the uncertainty condition would be randomly drawn from these uniform distributions by a computer at the end of the experimental session (i.e. participants were told that their group was equally likely to be any size between two and eight persons). The two conditions were counterbalanced to check for order effects. Preliminary analyses revealed no signifi cant order effects on any of the dependent variables (all F s < 1).

After the participants had read the instructions of the resource dilemmas, three practice questions were posed to ensure comprehension of these dilemmas. For example, participants were asked how much each group member would earn if the total group request exceeded the size of the collective resource; 99% of all participants answered all three questions correctly. After each question the correct answer was disclosed and the most important characteristics of the dilemmas were repeated. After that, the two dilemmas were presented.

Dependent measures

In each of the two (un)certainty conditions, participants requested a number of coins from the common resource. Additionally, under group size uncertainty they were asked to estimate the size of the group. At the end of the experimental session, which lasted about half an hour, all participants were debriefed, thanked, and paid for their participation. In the debriefi ng, we explained that we would pay all participants the same amount of money for their participation, namely 6 euros (i.e. approximately US$8), plus the extra money they had earned in one of the two resource dilemmas. All participants agreed with this payment procedure.

Results

Manipulation check All analyses were performed with 2 (SVO) × 2 (Group Size Uncertainty) analysis of variance (ANOVA) with repeated measures on the latter factor.

In each of the two conditions, we asked participants to indicate how uncertain they were about the size of the group (1 = very certain; 7 = very uncertain). A 2 × 2 ANOVA on this measure only yielded a highly signifi cant main effect of Group Size Uncertainty (F(1, 104) = 2417.61, p < .0001, η 2 = .96). As expected, participants were more uncertain about their estimates under Group Size Uncertainty (M = 6.25) than under No Group Size Uncertainty (M = 1.10). These results show that we were successful in manipulating group size uncertainty.

Individual requests

In each of the two conditions, the participants individually requested a number of coins from the common resource (see Table 1). A 2 × 2 ANOVA on participants' individual requests yielded a signifi cant main effect of SVO (F(1, 104) = 5.07, p < .05, η 2 = .05), which was qualified by a significant SVO × Group Size Uncertainty interaction effect (F(1, 104) = 6.18, p < .05, η 2 = .06). It should be noted, however, that in accordance with our expectations, the variance in the Group Size Uncertainty condition was considerably larger than the variance in the No Group Size Uncertainty condition. In order to reduce this heterogeneity of variances, we applied a square root transformation on participants' individual requests in all conditions. After applying this transformation, which successfully reduced the heterogeneity of variances, a 2 × 2 ANOVA still yielded a signifi cant main effect of SVO (F(1, 104) = 4.93, p < .05, η 2 = .05), and a significant SVO × Group Size Uncertainty interaction effect (F(1, 104) = 7.01, p < .01, η 2 = .06), as well as a signifi cant main effect of Group Size Uncertainty (F(1, 104) = 8.32, p < .01, η 2 = .07), which was also qualifi ed by the interaction.

To interpret the interaction effect, we tested whether the individual requests of proselfs differed from those of prosocials in each of the two Group Size (Un)certainty conditions. In accordance with Hypothesis 1, independent t tests on the individual requests showed no significant difference between proselfs and prosocials under No Uncertainty (M = 95.15 vs. 95.26, respectively) (t(104) = 0.02, p = .98). Under Uncertainty, however, prosocials requested signifi cantly lower amounts of coins than proselfs (M = 100.25 vs. 73.17, respectively) (t(104) = 2.55, p < .01). This latter fi nding corroborates Hypothesis 2. Further, we also looked at the effect of group size uncertainty for proselfs and prosocials separately. To do so, we conducted two separate repeated measures ANOVAs (i.e. one for each SVO) with Group Size Uncertainty as the independent variable (i.e. No vs. Yes) and individual requests as the dependent variable. These analyses showed that the requests of proselfs did not differ signifi cantly between the two (un)certainty conditions (F(1, 51) = .27, p = .61, η 2 = .01), whereas prosocials requested significantly lower amounts of coins in the Uncertainty condition than in the No Uncertainty condition (F(1, 53) = 18.44, p < .001, η 2 = .26). 1

Adherence to equality To assess to what degree participants anchored their decisions on the equal division rule, we investigated to what extent their individual requests deviated from an equal share. In the Uncertainty condition we calculated this equal share by dividing the resource size (i.e. 500 coins) by the participants' own group size estimates. After that, we calculated the absolute difference between participants' individual requests and this equal share (for a similar procedure to assess adherence to coordination rules, see e.g. [START_REF] Van Dijk | Decision-induced focusing in social dilemmas: Give-some, keep-some, take-some, and leave-some dilemmas[END_REF]. A 2 × 2 ANOVA on the deviation scores only yielded a signifi cant main effect of Group Size Uncertainty (F(1, 103) = 8.12, p < .01, η 2 = .07): participants' requests deviated signifi cantly more from an equal share under Group Size Uncertainty (M = 18.05) than under No Group Size Uncertainty (M = 7.98). This fi nding further corroborates our reasoning that under group size uncertainty people anchor their decisions less strongly on the equal division rule than under group size certainty.

Discussion

The data of Study 1 corroborate our hypotheses by showing the predicted interaction between SVO and group size uncertainty. Whereas both prosocials and proselfs harvested about an equal share under certainty, under uncertainty prosocials harvested less for themselves than proselfs. Furthermore, our data showed that prosocials decreased their harvests under group size uncertainty, whereas for proselfs the mean harvests remained the same.

But why did prosocials display self-restraint under group size uncertainty? To answer this question, it may be useful to take a closer look at the motives that may drive prosocials' decisions. Prosocials can be characterized by two main motives: they strive toward (a) equality in outcomes and (b) maximized joint outcomes (see e.g. [START_REF] Van Lange | The pursuit of joint outcomes and equality in outcomes: An integrative model of social value orientation[END_REF]. Therefore, it can be expected that these motives are important for them. However, the fact that these two motives are important for prosocials does not mean that these motives always explain their choice behavior. After all, although prosocials may be motivated to further both of these goals, they may not always be able to achieve them. For example, as we already argued in our introduction, equality is very diffi cult to apply under group size uncertainty (cf. De Kwaadsteniet, Van Dijk, Wit, De Cremer, & De Rooij, 2007). Thus, even if prosocials are highly motivated to achieve equality, they may not be able to do so under group size uncertainty, not even by displaying self-restraint. Furthermore, the second motive that characterizes prosocials, namely maximizing joint outcomes, does not necessarily imply selfrestraint either. Thus, whether either one of these motives drives prosocials' self-restraint under group size uncertainty remains an empirical question. Therefore, we decided to investigate this issue in a second study, in which we explicitly measure these two motives.

Study 2: The underlying motives of self-restraint

First, we predict the same interaction as in Study 1, that under group size certainty both prosocials and proselfs will harvest about an equal share from the common resource (see Hypothesis 1), whereas under group size uncertainty prosocials will show more self-restraint than proselfs (see Hypothesis 2). Second, we will test whether prosocials' self-restraint may be explained by either one of the two motives we described above, namely (a) the 'Equality' motive and (b) the 'MaxJoint' motive. And fi nally, we expect to replicate the fi nding of Study 1 that under group size uncertainty people deviate more from equality than under group size certainty (Hypothesis 3).

Method

Participants and design Participants were 78 students at Leiden University (42 men and 36 women, mean age = 20.95 years) who volunteered for the study. The design of Study 2 was identical to that of Study 1. Again, fi rst each participant's SVO was assessed (29 proselfs and 42 prosocials) and after that group size uncertainty was manipulated as a within-subjects factor. Accordingly, a 2 (SVO: Proselfs vs. Prosocials) × 2 (Group Size Uncertainty: No vs. Yes) factorial design with repeated measures on the latter factor was used.

Procedure The procedure of Study 2 was similar to that of Study 1. However, in this second study, after participants had made their individual requests, they were asked a number of questions to measure the motives underlying their harvesting decisions. Again, the two (un)certainty conditions were counterbalanced to check for order effects. Preliminary analyses revealed no signifi cant order effects on any of the dependent variables (all Fs < 1). Before participants were presented with the social dilemmas, we again posed the same three practice questions as in Study 1. This time, 97% of all participants answered all three practice questions correctly. At the end of the experimental session, participants were paid 6 euros (i.e. approximately US$ 8). They all agreed with this payment procedure.

Dependent measures

As in Study 1, in both (un)certainty conditions participants requested a number of coins from the common resource. After that, in each (un)certainty condition, two questions were posed about the motives that might have driven their decisions: (a) participants were asked to what extent they wanted their group to earn as much as possible (the 'MaxJoint' motive), and (b) they were asked to what extent they wanted the common resource to be distributed equally among the group members (the 'Equality' motive). 2 Both questions were answered on 7-point Likert scales (1 = not at all; 7 = very much so).

Results

Manipulation check

In each of the two (un)certainty conditions, we asked participants to indicate how uncertain they were about the size of the group (1 = very certain; 7 = very uncertain). A 2 × 2 ANOVA on this measure only yielded a highly signifi cant main effect of Group Size Uncertainty (F(1, 69) = 595.76, p < .0001, η 2 = .90). As expected, participants were more uncertain about their estimates under Group Size Uncertainty (M = 6.32) than under No Group Size Uncertainty (M = 1.44). These results show that we were successful in manipulating group size uncertainty.

Individual requests

As in Study 1, a 2 × 2 ANOVA on participants' individual requests yielded a signifi cant SVO × Group Size Uncertainty interaction effect (F(1, 69) = 5.13, p < .05, η 2 = .07), indicating that whereas prosocials' and proselfs' requests did not differ signifi cantly under No Uncertainty (M = 97.50 vs. 105.17, respectively) (t(69) = 1.21, p = .23), prosocials requested signifi cantly less than proselfs under Uncertainty (M = 84.95 vs. 122.69, respectively) (t(69) = 2.87, p < .01). 3,4 In other words, as we expected, under group size uncertainty prosocials showed more self-restraint than proselfs.

MaxJoint and equality

Two separate 2 × 2 ANOVAs on (a) the 'MaxJoint' motive and (b) the 'Equality' motive both yielded signifi cant main effects of Group Size Uncertainty (both Fs > 4.40, both ps < .05), and significant main effects of SVO (both Fs > 7.50, both ps < .01). These analyses indicated that under No Uncertainty participants were more motivated to achieve these two goals than under Uncertainty, and that prosocials were more motivated to achieve these goals than proselfs. This latter fi nding is in line with the defi nition of prosocials as fi nding both motives important. See Table 2 for the means involved in these analyses.

Which motive underlies self-restraint?

The main goal of Study 2 was to investigate which motive may have driven prosocials' self-restraint under group size uncertainty. To investigate this, we tested whether the effect of SVO on individual requests under group size uncertainty (i.e. that prosocials show more self-restraint than proselfs) was mediated by the two motives we mentioned above. This mediation analysis (see [START_REF] Baron | The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations[END_REF] showed that the effect of SVO on individual requests was fully mediated by the 'MaxJoint' motive (Sobel test value = -2.32, p < .05), but not by the 'Equality' motive. Although we would like to note that caution is warranted in interpreting such mediation analyses, these fi ndings seem to imply that prosocials' self-restraint under group size uncertainty may be explained by their motivation to maximize their group's outcomes.

Adherence to equality

As in Study 1, we also investigated to what degree participants anchored their decisions on the equal division rule in the two Group Size (Un)certainty conditions. Again, using their own group size estimates, we calculated to what extent their individual requests deviated from an equal share. As predicted, a 2 × 2 ANOVA on the (absolute) deviation scores yielded a signifi cant main effect of Group Size Uncertainty (F(1, 68) = 3.11, p < .05, η 2 = .04, one-sided). This main effect indicated that participants' requests deviated signifi cantly more from an equal share under Group Size Uncertainty (M = 16.86) than under No Group Size Uncertainty (M = 10.64). This fi nding corroborates Hypothesis 3, that under group size uncertainty people anchor their decisions less strongly on the equal division rule than under certainty.

Discussion

The data of Study 2 again showed the predicted interaction between SVO and group size uncertainty. Whereas both prosocials and proselfs harvested about an equal share under group size certainty, under group size uncertainty prosocials showed more self-restraint than proselfs. Furthermore, although our data showed that the Equality and MaxJoint motives are both important motives for prosocials (see Table 2), our mediation analyses suggested that the selfrestraint of prosocials (that was observed under group size uncertainty) can be understood by their motivation to maximize joint outcomes. Finally, we again showed that under group size uncertainty people deviate more from equality than under group size certainty.

General discussion

In the present article, we reported two experimental studies that investigated the infl uence of group size uncertainty and SVO in social dilemmas. Both studies corroborate our idea that group size uncertainty has important consequences for how people tacitly coordinate their behavior. Under group size certainty, people can effi ciently coordinate their behavior by applying the equal division rule. By contrast, under group size uncertainty tacit coordination is hampered because the task environment does not provide people with the salient cue to apply the equal division rule. In that case, people rely on internal cues (i.e. their SVO) to determine their harvesting decisions. Additionally, we demonstrated that, in contrast to earlier fi ndings on resource size uncertainty (e.g. Budescu et al., 1990;[START_REF] Gustafsson | Over-harvesting of resources of unknown size[END_REF], group size uncertainty does not necessarily induce overharvesting.

Thus, on the one hand our results show that group size uncertainty hampers effi cient coordination. At the same time, however, our results corroborate and extend [START_REF] Au | Effects of group size uncertainty and protocol of play in a common pool resource dilemma[END_REF] fi ndings by showing that group size uncertainty is not necessarily detrimental to collective interests, even when people make their harvesting decisions simultaneously (and they cannot know their fellow group members' decisions). Interestingly, whereas earlier research has shown that uncertainty about the size of the common resource leads to non-cooperative behavior, the present fi ndings indicate that uncertainty about the size of the group may even induce some people (i.e. prosocials) to show self-restraint. However, this fi nding raised the question as to why exactly group size uncertainty induced prosocials to show self-restraint. Was their self-restraint motivated by equality or by the motive to maximize joint outcomes? The fi ndings of Study 2 showed that, although both motives are important for prosocials, their selfrestraint may be explained by their motivation to maximize joint outcomes. These results indicate that the motive to maximize joint outcomes may have driven the self-restraint that we observed under group size uncertainty and perhaps also the self-restraint that Au and Ngai observed in their study.

Our data thus suggest that prosocials may have reasoned that under group size uncertainty self-restraint is benefi cial to the collective. But is self-restraint really a good means to maximize the group's outcomes? A plausible answer to this question can be found in Au and Ngai's paper (2003). In an appendix to their paper, they presented a calculative analysis that showed that in order to maximize group earnings, individual requests should decrease as the size of the group becomes more uncertain. More specifi cally, the expected utility for the group and its members is largest when all group members determine their harvesting decisions based on the largest possible group size. In other words, if group members want to maximize their group's payoffs, it is best to coordinate their individual harvests by dividing the common resource by the largest group size possible (i.e. in our singletrail resource dilemma they should each harvest 500/8 = about 60 coins). Thus, under group size uncertainty self-restraint indeed seems to be benefi cial to the collective interest.

As we already noted in the introduction to this article, the present research was strongly based on [START_REF] Au | Effects of group size uncertainty and protocol of play in a common pool resource dilemma[END_REF] paper on group size uncertainty. Our fi rst goal was to see whether their fi ndings would generalize to a resource dilemma with a simultaneous protocol. Therefore, we decided to use a social dilemma paradigm that closely resembled the one that was used by Au and Ngai. In this paradigm, participants have only one chance to harvest any amount of coins from the common resource. However, if the collective harvest exceeds the amount available in the common resource, no one receives anything (see also e.g. [START_REF] Budescu | Resource dilemmas with environmental uncertainty and asymmetric players[END_REF][START_REF] De Kwaadsteniet | Social dilemmas as strong versus weak situations: Social value orientations and tacit coordination under resource size uncertainty[END_REF]Gustafsson et al., 1999, for similar paradigms). Although this single-trial resource dilemma is often referred to as a social dilemma game, it also has some characteristics of a coordination game (see De [START_REF] De Vries | Constrained egoism and resource management under uncertainty[END_REF]. Therefore, the question remains as to whether the present results would generalize to other social dilemma paradigms. For instance, would people still show so much self-restraint if the consequences of over-harvesting were in the future, such as in a multiple-trial social dilemma with group size uncertainty? And does a multiple-trial dilemma-in which there is no clear absolute maximum total request-constitute a weaker situation than the single-trial dilemma we used in the present research? To investigate the generalizability of the present results, it is important to address these and other questions in future research.

It is also worthwhile to acknowledge the fact that the data of both studies provide fi rm support for the suggestion that [START_REF] Snyder | Personality and social behavior[END_REF] weak-strong distinction is highly applicable to social dilemma situations (see also De [START_REF] De Kwaadsteniet | Social dilemmas as strong versus weak situations: Social value orientations and tacit coordination under resource size uncertainty[END_REF][START_REF] Roch | Effects of environmental uncertainty and social value orientation in resource dilemmas[END_REF][START_REF] Van Lange | Movement in social orientations: A commentary on Kelley[END_REF]. In the present research, we showed that when the task environment of a social dilemma provides a salient cue to guide behavior, people will base their decisions on that cue (e.g. the equal division rule under group size certainty), whereas they will base their decisions on their own disposition when the task environment does not provide such a cue (e.g. their SVO under group size uncertainty). These fi ndings thus clearly show that Snyder and Ickes' framework (1985) on strong versus weak situations can be fruitfully used to explain and predict choice behavior in social dilemmas, and we therefore believe that future research may greatly benefi t from applying this framework to social dilemmas.

To summarize, the present studies have generated a number of interesting fi ndings. First, we showed that group size uncertainty-as opposed to resource size uncertainty-does not induce general over-harvesting and that this type of uncertainty is not necessarily detrimental to collective interests. After all, group size uncertainty induces prosocials to show selfrestraint under uncertainty. Second, we showed that group size uncertainty hampers effi cient coordination, inducing people to base their decisions on internal cues (i.e. their SVO) instead of external ones (i.e. the equal division rule), which corroborates the suggestion that [START_REF] Snyder | Personality and social behavior[END_REF] weak-strong distinction can fruitfully be applied to social dilemmas. And third, we showed that prosocials' self-restraint under group size uncertainty may be explained by their motive to maximize their group's outcomes. Taken together, by investigating the topic of group size (un)certainty in social dilemmas and relating this topic to tacit coordination and SVO, the present studies have generated a number of new insights into this largely unexplored type of environmental uncertainty.

Notes

1. These analyses were also done on proself and prosocials' transformed requests (i.e. transformed by applying square root transformations), which yielded the same results. 2. It may be interesting to note that we also measured to what extent participants were motivated to maximize their own outcomes (i.e. the 'MaxOwn' motive). As expected, we found that proselfs were more motivated by this motive than prosocials and that this motive was positively correlated with participants' harvests. However, a mediation analysis showed that this motive did not mediate the effect of SVO on harvests under group size uncertainty. 3. As in Study 1, we also conducted these analyses after applying a square root transformation. These analyses yielded similar results. 4. It should be noted that in contrast to Study 1, in Study 2 we did not fi nd a main effect of Group Size Uncertainty on individual requests (F(1, 69) = 0.14, p = 71, η 2 = .002). The mean requests seemed to be almost identical in the two (un)certainty conditions (M No Uncertainty = 100.63 vs. M Uncertainty = 100.37). This difference between the results of the two studies can be explained by the fact that whereas in Study 1 the requests of proselfs appeared to be unaffected by group size uncertainty, in Study 2 their mean requests increased slightly under uncertainty (from 105.17 coins to 122.69 coins). However, as in Study 1, prosocials still decreased their mean requests under group size uncertainty (from 97.50 coins to 84.95 coins) and they again showed self-restraint under such uncertainty.

Table 1 .

 1 Study 1: Individual requests by social value orientation and group size uncertainty

	Group size uncertainty

Notes: Higher scores denote higher individual requests. Standard deviations are given in parentheses.

Table 2 .

 2 Study 2: The 'MaxJoint' and 'Equality' motives by social value orientation and group size uncertainty Higher scores denote stronger motives. Standard deviations are given in parentheses.

			Group size uncertainty
		No		Yes
	Social value orientation	MaxJoint	Equality	MaxJoint	Equality
	Proselfs (n = 52)	4.55	4.93	3.79	4.55
		(1.76)	(2.05)	(1.74)	(2.06)
	Prosocials (n = 54)	5.43	6.00	5.17	5.40
		(1.64)	(1.34)	(1.62)	(1.59)
	Notes:


Dominic Abrams
email: d.abrams@kent.ac.uk

Michael A Hogg
email: michael.hogg@cgu.edu

Group Processes & Intergroup Relations 10 Years On: Development, Impact and Future Directions

Keywords: emotions, groups, intergroup relations, neuroscience, organizations, review

The development of this Journal, Group Processes & Intergroup Relations, is reviewed. Throughout its fi rst 10 years, the Journal has been supported by a strong editorial board. It has sustained a signifi cant profi le in social psychology in the area of both intergroup and small group processes. Its wider impact includes connection to related disciplines such as organizational behavior and neuroscience, focused special issues, small conferences related to the theme of the Journal and the expansion of group and intergroup research through learned societies. The editors thank authors, editorial board members, editorial assistants, reviewers and readers for their support.

Group Processes & Intergroup Relations (GPIR) is now at the end of its eleventh year (Vol. 11), our fi rst issue having been published in July 1998. When the Journal was launched, with the help of enthusiastic endorsements from Marilynn Brewer and Bib Latané, the international scene for communicating work on group processes and intergroup relations looked very different. Major U.S. journals in social psychology were providing only very limited space for research on groups, and specialist groups journals such as Small Group Research were concerned primarily with one sub-area. In Europe, both the European Journal of Social Psychology and the British Journal of Social Psychology were strongly representing work on social identity, social representations and other 'European' approaches but did not encompass much mainstream work from the USA. GPIR was launched to accomplish a truly international integration, to provide a home for a wider range of research, linking both small groups and intergroup processes, and encompassing both the European and non-European approaches.

At the time of its launch, the Journal was a controversial initiative and some European social psychologists were openly more enthusiastic than others. There were fears that the distinctiveness of the European and British journals might be undermined, and there were concerns that the apparent rise in interest in groups and intergroup relations might evaporate. As Editors we approached this issue empirically-we undertook an empirical review [START_REF] Abrams | Prospects for research in Group Processes & Intergroup Relations[END_REF]) that gave us confi dence that the Journal was going to represent a thriving and expanding area of research within social psychology. The fi nal article of the present issue [START_REF] Randsley | Prospects for Group Processes & Intergroup Relations research: A review of 70 years' progress[END_REF] expands and updates that empirical review and demonstrates that groups research has continued to expand, to become more infl uential in the major general journals in social psychology, and to have a very promising future. Far from weakening these mainstream journals, the arrival of GPIR has probably strengthened the position of groups research within them.

Our goal was for GPIR to act as the integrative focal point for groups research in all its diverse forms, and thus to invigorate the fi eld and raise the profi le and impact of this research across all social psychology journals. We feel this goal has been achieved.

The editorial board

The international scope and standing of the Journal has been supported through our stellar editorial board. We are enormously grateful for the guidance, support and work of our consulting editors and reviewers over the years, and especially to our associate editors.

Special issues

An important innovation for GPIR has been publication of special issues on themes that seemed particularly 'hot' at various times. The Journal remains open to proposals for special issues and will also act proactively to initiate special issues that seem timely. To date, we have published special issues on information processing in small groups [START_REF] Brauner | The information processing approach as a perspective for groups research[END_REF], social identity in organizations (van [START_REF] Van Knippenberg | Editorial: Social identity processes in organizations[END_REF], intergroup contact [START_REF] Dovidio | Intergroup contact: The past, present, and the future[END_REF], evolutionary approaches to group research [START_REF] Kameda | Evolutionary/ adaptive thinking as a meta-theory for systematic group research: An extended 'fungus-eater' approach[END_REF], the inaugural group processes and intergroup relations pre-conference of SPSP [START_REF] Gaertner | Group and intergroup processes: An introduction[END_REF], workplace diversity [START_REF] Christian | Workplace diversity and group relations: An overview[END_REF], lay theories and intergroup relations [START_REF] Levy | Lay theories and intergroup relations[END_REF], intergroup emotions (Giner-Sorolla, Mackie, & [START_REF] Giner-Sorolla | Special issue on intergroup emotions: Introduction[END_REF] and social neuroscience and intergroup behavior [START_REF] Prentice | The neural underpinnings of group life[END_REF]. Forthcoming issues include music and intergroup relations (Giles, Hajda, & Hamilton), dehumanization(Castano & Kofta) and selfregulation within and between groups ( Jonas, Sassenberg, & Scheepers).

Impact and expansion of the Journal

A signifi cant success for the Journal was its inclusion in the ISI indexes relatively early (after Volume 6-2003). The Journal hit the ground running in 2006 with an impressive impact factor of 1.58 (13th of the 48 journals in the Thompson Social Science Citation Index for social psychology). This year GPIR registered an impact factor of 1.49.

The spread of citations across content suggests that the scope of the Journal is even and appropriate. From Volume 1 the three most cited articles cover leadership, group investment and group processes [START_REF] Abrams | Prospects for research in Group Processes & Intergroup Relations[END_REF][START_REF] Platow | Leadership endorsement: The role of distributive and procedural behavior in interpersonal and intergroup contexts[END_REF][START_REF] Smith | Investment decisions by individuals and groups in 'sunk cost' situations: The potential impact of shared representations[END_REF]. In Volume 2 the most cited articles were on crossed categorization, positive negative asymmetry and schism [START_REF] Buhl | Positive-negative asymmetry in social discrimination: Meta-analytical evidence[END_REF][START_REF] Crisp | Differential evaluation of crossed category groups: Patterns, processes, and reducing intergroup bias[END_REF][START_REF] Sani | Identity, argument and schism: Two longitudinal studies of the split in the Church of England over the ordination of women to the priesthood[END_REF]. In Volume 3 the most cited articles were on collective effi cacy, work groups and shared representations [START_REF] Hollingshead | Perceptions of expertise and transactive memory in work relationships[END_REF][START_REF] Peterson | Collective effi cacy and aspects of shared mental models as predictors of performance over time in work groups[END_REF][START_REF] Tindale | Social sharedness' as a unifying theme for information processing in groups[END_REF]. The most cited articles in Volume 4 were on intergroup attitudes, organizational merger and hostile media [START_REF] Brown | Life on the ocean wave: Testing some intergroup hypotheses in a naturalistic setting[END_REF][START_REF] Matheson | Social identity precursors to the hostile media phenomenon: Partisan perceptions of coverage of the Bosnian confl ict[END_REF][START_REF] Terry | Legitimacy and ingroup bias in the context of an organizational merger[END_REF]. From Volume 5, the most cited article was on deviance [START_REF] Abrams | Anti-norm and pro-norm deviance in the bank and on the campus: Two experiments on subjective group dynamics[END_REF], and from Volume 6 the most cited articles were on intergroup contact [START_REF] Levin | The effects of ingroup and outgroup friendships on ethnic attitudes in college: A longitudinal study[END_REF][START_REF] Shelton | Interpersonal concerns in social encounters between majority and minority group members[END_REF][START_REF] Voci | Intergroup contact and prejudice toward immigrants in Italy: The mediational role of anxiety and the moderational role of group salience[END_REF]. These fi rst six volumes provided the basis for the calculation of the initial impact factor of GPIR.

In Volume 7, articles on intergroup emotions [START_REF] Miller | Effects of intergroup contact and political predispositions on prejudice: Role of intergroup emotions[END_REF][START_REF] Navarrete | Anxiety and intergroup bias: Terror management or coalitional psychology?[END_REF], and evolution and xenophobia [START_REF] Faulkner | Evolved disease-avoidance mechanisms and contemporary xenophobic attitudes[END_REF] were most highly cited. In Volume 8, the most cited articles were on reducing intergroup bias [START_REF] Crisp | Reducing intergroup bias: The moderating role of ingroup identifi cation[END_REF] and intergroup emotion [START_REF] Lickel | Vicarious shame and guilt[END_REF] and perspective taking [START_REF] Galinsky | Perspective-taking and self-other overlap: Fostering social bonds and facilitating social coordination[END_REF]. The most cited articles from Volume 9 were on implicit theories [START_REF] Haslam | Psychological essentialism, implicit theories, and intergroup relations[END_REF], general prejudice [START_REF] Jayaratne | White Americans' generic lay theories of race differences and sexual orientation: Their relationship with prejudice toward blacks, and gay men, and lesbians[END_REF] and intergenerational contact [START_REF] Tam | Intergroup contact and grandparent-grandchild communication: The effects of self-disclosure on implicit and explicit biases against older people[END_REF] In line with other journals, GPIR has increased its page extent (from approximately six articles per issue to nine or ten), and from 2009 we will be increasing the number of issues per volume from four to six. This refl ects a healthy increase in the volume of submissions. We also moved to an on-line manuscript-tracking system in 2008 which has resulted in a faster manuscript decision time (currently under 90 days).

Group processes and intergroup relations pre-conference at the SPSP annual conference

The annual conference of SPSP is the world's largest annual gathering of social psychologists. Initially, there were no groups pre-conferences, so in 2004 Lowell Gaertner, Michael Hogg and Scott Tindale initiated the inaugural group processes and intergroup relations pre-conference. It has become a very successful and stimulating annual one-day event; an opportunity for groups researchers to meet one another, and a valuable companion activity for GPIR. Subsequent pre-conferences have been convened by Hinsz, Dovidio and Park, Brewer, Craig and Crisp, Castano, Miller and Jackson, and Hogg, Levine and Blaylock. Attendance has risen from 63 in 2004 to 125 in 2008. Parallel pre-conferences have been run recently at both SESP and EAESP, signalling the fi rm establishment of the 'group processes and intergroup relations' as a coherent focus and body of research.

Conclusions, prospects and thanks

We hope that readers of GPIR will agree that the Journal has made excellent progress since its inception. The prospects continue to look good as the number of manuscripts being submitted is increasing and the quality of the work is extremely high. We intend to increase the size of the associate editorial team to refl ect these trends. In common with other journals, we intend to ensure as fast a decision time as possible, and this will sometimes mean that editors may have to make decisions with only one or two reviews to hand, though we will sustain a policy of seeking three reviews for each decision. There are many new and exciting areas of research in group processes and intergroup relations. A key challenge that remains is how best to integrate and combine theories of small group, intragroup processes with theories of intergroup processes. These two levels of analysis are proximal, but researchers are also becoming more interested in how these can be connected with higher and lower levels (e.g. sociological and anthropological, on the one hand, and biological and neuroscience, on the other hand). Additional questions concern the way in which affective and cognitive processes combine in groups, how people learn about group processes (e.g. as they move between groups with different norms, and as they develop over their lifespan) and the role of groups in motivating and constraining people's abilities and performance.

Research funding, at least in North America and Europe, appears to be pitched increasingly at work that integrates across disciplines, cultures and methods. Some parts of social psychology may be able to evade these pressures, but work on group processes and intergroup relations necessarily falls at the intersections of many areas. There is also increasing pressure towards translational and transformational research-research that is more accessible, more immediately relevant to social issues and more likely to transform our world in positive ways. As society itself becomes more complex, more global and more interconnected, there has never been a more important time to focus on how people combine to behave toward one another as members of different social groups. These issues bear directly on how we can deal with, for example, inequality, terrorism, global environmental and health threats, collective decision making, and population movement and culture clashes. We hope that GPIR will be able to capture and promote the best research addressing these and other questions.

As editors of this Journal it has been our honour to work with such distinguished colleagues. It is very satisfying that the readership and impact of the Journal continues to grow. Advising and urging us through the initial practical steps we benefi ted especially from invaluable guidance by Dick Moreland and Jack Dovidio. Much work has also been done by a series of very dedicated and patient editorial assistants, many of whom now hold permanent academic posts themselves. Our fi rst editorial assistant was Barbara Masser, followed by Sabina Aharpour, Georgina Randsley de Moura, Lindsey Cameron, Katerina Tasiopoulou, and currently Joe Pelletier. Their commitment and energy has been essential for the success of the Journal. Finally, we are tremendously grateful to Ziyad Marar and Michael Carmichael from SAGE Publications whose confi dence and enthusiasm has been essential and greatly valued since the inception of the Journal.

  Personality and Social Psychology Bulletin and others. Several have also held presidencies or other key positions on the committees of learned societies including the European Association of Experimental Social Psychology (EAESP), the Society for the Psychological Study of Social Issues (SPSSI), the Society for Personality and Social Psychology (SPSP), and the Society for Experimental Social Psychology (SESP). Both the associate editorial team and the consulting editors are invited as a refl ection of the content of the articles submitted to the Journal, and also to signal to the academic community what GPIR wants to represent. It has been, and continues to be, a great pleasure working with our colleagues in these roles.

	established our current team, which includes
	Bertjan Doojse, Matthew Hornsey, Norbert Kerr
	and Linda Tropp. Many of these outstanding
	researchers have held major editorial roles in
	journals such as Journal of Personality and Social
	Psychology,
	Volume 1 was launched with a very able and
	expert team (Anne Maass, John Dovidio, Diane
	Mackie, Richard Moreland, Don Taylor and Scott
	Tindale). Victoria Esses joined for Volume 2,
	Margo Monteith and Carsten De Dreu at
	Volume 4, and Nyla Branscombe for Volume 6.
	Emanuele Castano, Craig Parks and Deborah
	Prentice joined for Volume 8, Serge Guimond
	and Brenda Major for Volume 9. Volume 10

Acknowledgments

We are grateful to Georgina Randsley de Moura, Michael Carmichael and Francis Samra for their comments and assistance with the preparation of this article.