Majority Decision Making Works Best under Conditions of Leadership Ambiguity and Shared Task Representations

Word count: 169 Abstract The effectiveness of decision-making teams depends largely on their ability to integrate and make sense of information. Consequently, teams which more often use majority decision making may make better quality decisions, but particularly so when they also have task representations which emphasize the elaboration of information relevant to the decision, in the absence of clear leadership. In the present study I propose that (a) majority decision making will be more effective when task representations are shared, and that (b) this positive effect will be more pronounced when leadership ambiguity (i.e. team members’ perceptions of the absence of a clear leader) is high. These hypotheses were put to the test using a sample comprising 81 teams competing in a complex business simulation for seven weeks. As predicted, majority decision making was more effective when task representations were shared, and this positive effect was more pronounced when there was leadership ambiguity. The findings extend and nuance earlier research on decision rules, the role of shared task representations, and leadership clarity. Contribution to the field Prior research on team decision making has shown that shared task representations play an important role in the effective use of information resources in groups. However, the role of decision-making procedures and rules in team decision making has received very little research attention, along with the role of leadership clarity/ambiguity in such contexts. The current paper contributes to this field of research by studying the relationship between the use of a majority decision rule and performance as moderated by task representations and leadership clarity (and the lack thereof, leadership ambiguity). As hypothesized, the results showed that majority decision making was positively related to team performance when a high level of elaboration on information was combined with leadership ambiguity. However, under conditions of low elaboration of information, and leadership ambiguity, majority decision making was negatively related to performance. This is an important contribution to the research on leadership clarity, as it shows that under some circumstances low leadership clarity (i.e. leadership ambiguity) can be beneficial for team performance. These results also show that the relationship between decision rules and performance is more complex than previous research has suggested, as majority decision making can be sometimes positively, and sometimes negatively related to performance, with the relationship moderated by other team processes.


Introduction 22
"When exploring the Northwest Territory in 1805, Captain Clark used the majority rule 23 to decide where to set his winter camp (Ambrose, 1996;Moulton, 2003). Everyone in 24 the expedition, including servants and native guides, had an equal vote in the 25 majority rule decision." 26 - (Hastie & Kameda, 2005, p. 506). 27 As Hastie and Kameda noted, the "robust beauty of the majority rule" may explain its 28 popularity in today's teams as well as in primordial societies. This rule indeed has many virtues: 29 transparency, ease of execution, it appeals to people's innate sense of justice, and it often yields more 30 effective solutions to problems. When no explicit rule is established, the implicit decision rule is 31 essentially a majority rule (Hastie & Kameda, 2005). Organizations nowadays often rely on teams 32 when making decisions that require a wide array of knowledge (Dooley & Fryxell, 1999;Kozlowski 33 & Bell, 2003). The effectiveness of those decision-making teams is for a large part dependent on the 34 I n r e v i e w decision rules they apply (Hastie & Kameda, 2005;Nitzan & Paroush, 1985;Stasser, Kerr, & Davis, 35 1980), and on their ability to make use of and integrate information successfully (e.g., M. C. 36 Schippers, Homan, & van Knippenberg, 2013; van Ginkel & van . Although 37 theoretically teams should be better suited to make use of information and should make better 38 decisions, numerous studies have shown that groups often fail to exchange information (Gruenfeld,39 Mannix importance of those representations for information elaboration and decision making, it has not 48 focused on an important antecedent of team decision making and performance: decision-making 49 procedures or rules. Teams often agree on a strategy to make decisions. A commonly used decision 50 rule is majority decision making (Baron, Kerr, & Miller, 1992), but the task requirements often 51 determine for a large part which decision making procedure is more effective (Beersma & De Dreu,52 2002; F. S. Ten Velden, . For instance, pooling preferences and making 53 compromises may be an ineffective way of making majority decisions (van Ginkel & van 54 Knippenberg, 2008). Faced with a (unanimous) majority, other team members may think from the 55 perspective of the majority and may exclude other considerations, due to the stress that is caused by 56 being in the minority (Stasser & Birchmeier, 2003). A critical thought norm may offset the possible 57 negative sides of a decision making rule (Postmes, Spears, & Cihangir, 2001). Shared task 58 representations may thus be especially relevant when teams apply a majority rule to make decisions, 59 such that the integrated information is used in making the final decision (F. S. Ten Velden, Beersma, 60 & De Dreu, 2007). Depending on the team task, for instance if teams have to make decisions that 61 influence each other (e.g., a company decision to buy more machines may also mean having to hire 62 personnel to run the machine), may make sure that team members voice their opinion, even if they 63 are in the minority. 64 Another factor that may determine the extent to which team members voice their opinion is 65 team leadership. The combination of shared task representations and a majority rule will prove 66 especially fruitful in teams without a clear leader, and thus leader ambiguity (cf. Carson,Tesluk,& 67 Marrone, 2007; West et al., 2003). In such groups, clarity of leadership -that is, team members' 68 shared perceptions of clarity and the absence of conflict over leadership of their teams (West et al.,69 2003)may be a liability rather than an asset, since a clear leader may have an uneven impact on the 70 decision to be made (e.g., I. L. Janis, 1972; I. L. Janis, 1982), and may cause "closing of the group 71 mind" (cf. De Grada, Kruglanski, Mannetti, & Pierro, 1999;Kruglanski & Webster, 1991;Tetlock, 72 2000). Thus, groups without a clear leader may be at an advantage when they have shared task 73 representations and a majority rule, as they may make use of information better when making a 74 decision. In the current paper, I will argue that the extent to which teams make use of a majority 75 decision rule will be positively related to team performance under conditions of high shared task 76 representations and lack of leadership clarity, which I will name leadership ambiguity in the 77 remainder of the paper (see Figure 1).  The current study makes a number of contributions to the literature on team decision making  84  and on the broader team performance literature. Specifically, it puts majority decision making and  85  leadership ambiguity center-stage in the study of team decision making, and does so in the controlled  86 context of a management simulation. Furthermore, it points to the importance of shared task 87 representations, with an emphasis on sharing, discussing and integrating information. The current 88 study points to the fact that it is the combination of those three factors that determine group 89 outcomes, rather than isolated effects of any one of those variables. Specifically, teams can improve decision making by discussing and exchanging information in the 106 group, and this is also related to "social sharedness" (Scott & Kameda, 2000 Schippers et al., 2013), and the development of shared task representations that 117 emphasize information elaboration may therefore be key to team success. This may be especially so 118 when the team tends to favor majority decision making, because then the team members will be more 119 motivated to "defend" their ideas and findings and will take more trouble to elaborate information. 120 This may be especially so in the context of a management simulation, where decisions need to be 121 discussed, because a decision made in one domain, influences the effectiveness of other decisions, 122 and there is a clear need to align decisions. 123 Hypothesis 1: Shared task representations will be positively related to team performance 124 125 I n r e v i e w 2.2 Majority decision making and team performance: The moderating role of shared task 126 representations 127 Decision-making procedures or rules may affect the way teams make decisions and this may 128 help or hinder team performance (Bianco, Lynch, Miller, & Sened, 2006). A group decision rule 129 specifies how decisions are made within a team, and can be defined as "a rule that specifies, for any 130 given set of individual preferences regarding some set of alternatives, what the group preference or 131 decision is regarding the alternatives" (Miller, 1989, p. 327). The two rules used most often in groups 132 are the majority rule and the unanimity rule (Baron et al., 1992;Hare, 1976;Miller, 1989b), although 133 it is also conceivable that a directive team leader or dominant group member makes most of the 134 decisions (cf. Leana, 1985;Van de Ven & Delbeco, 1971). Because unanimity requires agreement 135 from all team members, group decisions may be harder to reach and require more discussion (e.g., 136 Castore & Murnighan, 1978; Miller, 1989a). Teams which make many decisions in a practical or 137 simulation context may therefore find a majority decision rule to be more efficient and less time-138 consuming (Hare, 1976;Kerr et al., 1976), and this rule seems to be indeed most prevalent for intact 139 teams, as it induces team members to behave in the interest of the group (e.g., Tatsuya  In short, for teams facing a complex task, and high on leadership ambiguity, majority decision 236 making will positively influence team performance when the team also has shared task 237 representations that emphasize information elaboration. 238 Hypothesis 3: Shared task representations and leadership clarity/ambiguity will jointly 239 moderate the relationship between the extent of majority decision making and team 240 performance, such that: 241 (a) When shared task representations are high, combined with leadership ambiguity, the 242 relationship between majority decision making and team performance will be positive.

243
(b) When shared task representations are low, combined with leadership ambiguity, the 244 relationship between majority decision making and team performance will be negative 245 (c) For other combinations of shared task representations and leadership ambiguity, there will be 246 no difference in team performance under conditions of high or low majority decision making. 247 248 3 Methods 249

Sample and procedure 250
Data for this study were collected by means of a survey handed out to all team members as 251 part of a larger investigation involving teams taking part in a supply chain business simulation. delivery problems, special customized products, etc. Teams were expected to integrate and make 308 I n r e v i e w sense of all this information in order to reach decisions and make choices (for a screenshot of the 309 game, See Figure 2). Many decisions are made when playing the game, and trade-offs were implied 310 in every decision. The extent to which teams were able to balance these trade-offs, determined their 311 performance (ROI) 312 The game started with a video message from the former CEO, who explained current issues in 313 the company. Team decisions were uploaded and processed and the simulation then provided a 314 weighted team-performance composite for each round. Furthermore, the teams received detailed 315 feedback reports (for an elaborate descripion of the game see De Leeuw et al., 2015). 316

Measures 317
After the participants had completed the game, but before they received feedback on their 318 final performance, they filled in a survey that measured various team processes (see Appendix for all 319 items used in the survey). 320 your team?" They were requested to select one of the following options: "There is a very clear 337 leader/coordinator", "A number of people lead/coordinate the team", "There is no clear 338 leader/coordinator", "There is conflict over who leads/coordinates the team" and "We all have 339 leadership roles". Following West et al. (2003), leadership clarity was measured by the proportion of 340 respondents who either said: "There is no clear leader/coordinator" or "There is conflict over who 341 leads/coordinates the team". Since none of the teams indicated that there was conflict over who was 342 leading the team, leadership ambiguity was calculated to represent the proportion of team members 343 indicating that there was no clear leader or coordinator. 344 Team Performance. Team performance in the simulated game was assessed by the team 345 score of Return on Investment (ROI) of the fictitious company. The objective for each team is to 346 achieve the best return on investment (ROI). It was not only crucial to make as much money as 347 possible, but also to manage investments in a proper way (see also De Leeuw et al., 2015). As each 348 round represented a decision horizon of six months, the focus of the game is on strategic and tactical 349 supply chain decisions (for a screenshot of the game, see Figure 2). After each round participants 350 could see their performance and compare with other teams in the competition. Each round players 351 make progressively more difficult decisions, as complexity is gradually added each round. It is key 352 for teams to choose a strategy and to make decisions in accordance to the chosen strategy. 353 I n r e v i e w Furthermore, performance in each round is calculated independently, and teams do not suffer 354 negative consequences resulting from poor decisions, or profit from very good decisions made in 355 earlier rounds (De Leeuw et al., 2015). 356 The simulation automatically calculated a team's overall score by indexing each factor on a 357 scale of -1 to 1, according to the team's relative performance in the simulation. The final score 358 represented a weighted average of the score over six rounds, where the last two rounds were the most 359 important in determining the final score for the team, and the lowest score was discarded. The scores 360 on ROI can be seen as a percentage score (similar to other simulations, (e.g., Mathieu & Rapp, 2009), 361 and varied from -0.46 to 0.17, M = 0.03, SD = 0.11. In addition to the team score there also is an 362 individual score for each role in the team. These individual scores do not count toward the team 363 score, but did allow participants to compare their performance relative to peers in other (competing) 364 teams. 365 Results 370

Data aggregation 371
Our theory and measurement were aimed at the team level of analysis, with the dependent 372 variable of interest being a team-level variable, ROI. Although in the current study individuals were 373 nested within groups, multilevel techniques were not applied, as for these analysis the dependent 374 variable needs to be at the lowest level of analysis (in this case the individual level; (Bryk & 375 Raudenbush, 1992). Although individual level scores were provided in the game, these scores did not 376 determine the outcomes, as cross-functional integration and a clear strategy were key for 377 performance in the game. Because the present study focused on a group-level dependent variable 378 (i.e., team performance), aggregation to the group level is the most appropriate strategy to analyze the 379 data (Kashy & Kenny, 2000). As presented above, the ICC(1) value and the rwg(j) value were 380 sufficient to justify aggregation (P.D. Bliese, 2000;James, Demaree, & Wolf, 1984. Since the 381 ICC(2) value also depends on team size, with higher values of ICC(2) as team size increases (P.D. 382 Bliese, 2000), I chose to depend mainly on the outcomes of ICC(1) in deciding whether or not to 383 aggregate the individual-level scores. I therefore used the mean (i.e. the average; see also Barrick,384 Stewart, Neubert, & Mount, 1998) of the team members' scores to represent shared task 385 representations at the team level. This was not the case for majority decision making, and team 386 leadership ambiguity, as these had discrete answer categories, and not a relative score. 387 388

Descriptive statistics 389
As can be seen in Table 1, age is positively related to experience (r =.20, p < .05), knowledge 390 of supply chain management (SCM) (r =.27, p < .05), shared task representations (r =.31, p < .01), 391 and team performance (r =.20, p < .05). Gender is negatively related to SCM knowledge (r = -.31, p 392 < .01). Also, the hours spent on playing the game are positively related to shared task representations 393 (r =.18, p < .05), but not significantly positively related to team performance (r =.13, ns). Teams with 394 a lot of SCM knowledge seemed to opt for majority decision making slightly less (r =-.21, p < .05), 395 possibly because it was easier for them to reach a consensus decision. Finally, shared task 396 representations are positively related to team performance (r =.23, p < .05), while the extent to which 397 I n r e v i e w teams opt for majority decision making is negatively related to team performance (r =-.22, p < .05). 398 This may indicate that teams choosing a majority rule have more problems in making decisions and 399 opt for this rule in order to make a decision 3 . 400

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Insert Table 1 about here  402 - Prior to the analyses, all continuous independent variables were mean-centered (Aiken & West, 405 1991). The hypotheses suggest one two-way interaction, and one three-way interaction, and we tested 406 whether each interaction added unique variance by testing them in one model. Table 2 reports the 407 series of regression models to test both the main effect of shared task representations on team 408 performance and the hypothesized moderator effects. In each regression analysis, the control 409 variables are entered as the first step. 410 In line with Hypothesis 1, hierarchical regressions showed that there is a significant, positive 411 relationship between shared task representations and team performance (β = .23; p < .05; see model 412 3), however this relationship is only significant in combination with the two-way interaction. When 413 the three-way interaction is added in model 4, this relationship is no longer significant. Hypothesis 2 414 predicted an interaction between majority decision making and shared task representations that 415 emphasize information elaboration. Hierarchical regressions indeed showed that this predicted 416 interaction was indeed significant (β = .25; p < .05; see Figure 1). To determine the nature of this 417 interaction, we performed simple slopes analysis (Aiken & West, 1991). These tests showed that for 418 teams with relatively high shared task representations (one SD above the mean), a positive 419 relationship between majority decision making and team performance was found; t = 2.71, p < 001. 420 For teams with relatively low shared task representations (one SD below the mean), this relationship 421 was negative; t = -5.01, p < .001. This indicated that under conditions of high majority decision 422 making, shared task representations that emphasize information elaboration are related to higher team 423 performance. Hypothesis 3 implied a three-way interaction between majority decision making, shared task 428 representations that emphasize information elaboration and leadership ambiguity. Hierarchical 429 regressions showed that this predicted interaction was indeed highly significant, (β = .32, p < .01; see 430 Table 2, and Figure 2). Visual inspection of the figure indicates that team performance is highest 431 when majority decision making is high, and when high task representations are combined with high 432 leadership ambiguity. A combination of low task representations and high leadership ambiguity is 433 related to low team performance. Simple slope analyses showed that when task representations were 434 low (one SD above the mean) and leadership ambiguity was low, the slope of low task 435 representations/high leadership ambiguity was significant (t = -4.75, p < 001). The slope of high task 436 representations and high leadership ambiguity was only marginally significant (t = 1.83, p = .07). As 437 expected, the slope difference test was insignificant for low task representations/low leadership 438 ambiguity (t = .23, ns) and for high task representations/ low leadership ambiguity (t = .01, ns). In 439 addition, slope difference tests were calculated for all six pairs of the slopes (J. F. Dawson & Richter,440 2006). These allow for comparative tests between sets of slopes, as opposed to the absolute tests of 441 single slopes calculated by the simple slope analyses presented above (J. F. Dawson, 2014). These 442 I n r e v i e w tests indicated that that there are significant differences for three pairs of slopes. The difference 443 between slope 1 (high shared task representation/high leadership ambiguity) and slope 3 (low shared 444 task representation/high leadership ambiguity) was significant (t = 3.88, p < .001). The difference 445 between slope 2 (high shared task representation/low leadership ambiguity) and slope 3 (low shared 446 task representation/high leadership ambiguity) was also significant (t = 2.35; p < .05), and finally the 447 difference between slope 3 (low shared task representation/high leadership ambiguity) and 4 (low 448 shared task representation/low leadership ambiguity) was also significant (t = -2.73; p < .01). Overall, 449 it seems that the combination of low shared task representation with high leadership ambiguity 450 differed significantly from all other slopes. These findings indicate that especially under conditions 451 of high majority decision making, a combination of shared task representations that emphasize 452 information elaboration and high leadership ambiguity is positively related to performance.

Pattern of results 458
Decision-making groups with a complex task and distributed information often do not make 459 optimal use of their informational resources (Stasser & Birchmeier, 2003). The decision rule used by 460 the team may be of the utmost importance, but cannot be seen in isolation from other aspects of 461 group process and leadership, i.e. task representations that emphasize elaboration of decision-relevant 462 information, and leadership ambiguity. The current study showed that (perceptions of) majority 463 decision making was related to superior team performance when teams were also high on shared task 464 representations that emphasize elaboration of information. A three-way interaction showed that a 465 high level of majority decision making was positively related to superior team performance when a 466 high level of elaboration on information was combined with leadership ambiguity. High majority 467 decision making was related to a lower level of performance under conditions of low elaboration of 468 information, combined with leadership ambiguity. Although the simple slope analysis indicated that 469 especially the combination of a low level of shared task representations/ leadership ambiguity is most 470 explanatory under conditions of low versus high majority decision making, the slope difference tests 471 showed that the this particular slope was significantly different from the combination of high level of 472 shared task representations/ leadership ambiguity. Moreover, these two slopes differed significantly 473 from the other two slopes (high shared task representations/low leadership ambiguity and low shared 474 task representations/ high leadership ambiguity  Kameda, 2005). If a decision is made opting for a majority rule, then a manager or leader should be 497 less prominent or even absent. Also, such a decision should be made in teams that have task 498 representations emphasizing elaboration information. 499 Theoretically, it should be noted that authority differentiation, or the extent to which all team 500 members are involved in team decision making processes (Hollenbeck,Beersma,& Schouten,501 2012), has some similarities to majority decision making. However, in the context of the current 502 paper, I was especially interested in the rules that teams use to make decisions. Thus, while authority 503 differentiation can be related to the process of decision making, and the extent of involvement of 504 team members in this process, a decision rule may still be implied to make the actual decision. Future 505 research could focus on the role of authority differentiation that precedes decision making. 506

Limitations and future directions 507
While an obvious strength of the current study is that I tested the hypotheses with a large 508 number of teams, comprising mainly of professionals in a realistic setting, we should recognize that 509 only experimental studies can speak to the causality implied in the research model. A clear direction 510 for future research would thus be to follow this work up in experimental designs, manipulating 511 decision rules, shared task representations and leadership ambiguity. Also, not all teams were 512 experienced in the field of supply chain management, although I did control for this in the analysis. 513 A limitation of sorts is that while I do indeed have evidence of the core team processes and 514 decision rules involvedshared task representations, majority decision making, and leadership 515 ambiguityhow that played out in practice is not completely clear. That is, I do not know exactly 516 what happened in teams with leadership ambiguity, and whether in teams with leadership ambiguity 517 there was indeed more room for elaboration of task-relevant information. Furthermore, elaboration of 518 information might also have taken place more implicitly, as team members could also elaborate 519 information as a habitual practice without conscientious, or explicit awareness. Also, the question is 520 whether teams performing well in the game, also perform well in the real world. While evidence in 521 this respect is not required for the test of our hypothesesnor is any specific content suggested by 522 our analysissuch information could be extremely helpful in further developing our analysis, as it 523 may provide key pointers as to as to what factors influence the effectiveness of majority decision 524 making. Future research to address this issue would therefore be very valuable. 525 Also, it should be noted that none of the teams reported conflict over leadership. While an 526 earlier study found leadership ambiguity to be a combination of "there is no clear leader/coordinator" 527 and "there is conflict over who leads/coordinates the team", (West et al., 2003) in the current study 528 this variable denoted solely the absence a clear leader/coordinator, since none of the team members 529 indicated conflict over leadership. Hence, our results may slightly differ from those earlier results, for 530 instance the finding that leadership ambiguity was negatively related to team processes and team 531 I n r e v i e w innovation (West et al., 2003). In the current study, leadership ambiguity as such was unrelated to 532 team performance. The absence of conflict over leadership may have ensured there was no direct 533 negative relationship. Also, the dependent variable in the study of West et al. (2003) was innovation, 534 and it could be that leadership ambiguity is more negatively related to innovation than to team 535 performance. Future research could incorporate both innovation and performance as dependent 536 variables. 537 Another limitation has to do with the reporting of moderated multiple regression (MMR). 538 Recent theorizing discussed the fact that these analyses often report small effect sizes, as well as 539 often being underpowered (Murphy & Russell, 2017

Conclusion 559
The current study integrates and extends theorizing on the relationship between decision rules 560 and team processes. Since the use of decision rules can greatly influence the team process and 561 outcomes (e.g., Hastie & Kameda, 2005), it is imperative to know the contingencies of the 562 relationship between decision rules and team performance. My analysis has shown that the 563 relationship with performance is not a simple one. Under conditions of high majority decision 564 making, the relationship with team performance is moderated by both task representations and 565 leadership ambiguity. The implication for those interested in optimizing team performance is that, 566 for complex decision-making tasks, to make optimal use of the majority decision rule, task 567 representations emphasizing information elaboration should be high, while leadership ambiguity 568 should be high. Footnotes 825 1 One of the reviewers noted that it would be hard to predict an exact shape of interactions, and that it 826 would be good to elaborate on this issue in the introduction. Note that although I did predict a two 827 and three-way interaction, the exact shape was hard to predict from existing theory. I did have a 828 general idea of what the shape would be before I gathered the data. However, in rewriting this paper, 829 I also rewrote the hypotheses (thanks to the reviewer for the helpful suggestion), and thus used a 830 combination of a priori reasoning and abduction (Behfar & Okhuysen, 2018). The overall shape of 831 the interactions was as predicted. 832 833 2 Two other options, added by the game provider, were "We argued a lot about the decisions we had 834 to make" and "We often agreed quickly". Hardly any teams opted for these, and adding these options 835 as control variables did not change our pattern of results. When we added a unanimity rule of 836 collective decision making ("All decisions were made as a team") as a control variable to the 837 regression analysis, our pattern of findings also remained unchanged. 838 839 3 Note that the extent to which teams indicated that "there is a very clear leader" was as expected 840 negatively related to leadership ambiguity (r = -.616, p<.001). Although we could have opted for 841 collapsing these items, for this paper we chose to stick to the item as used in prior literature. 842 For the items on decision making rules, only the items on unanimity rule (All decisions were made as 843 a team) and majority rule (We had a majority rule) were relatively highly correlated (r=-.513 p<.001). 844 The relationship between majority decision making and one dominant team member making all 845 decisions was rather low, and not significant (r=-.124; ns). Since I was interested in the effect of 846 majority rule (and not the unanimity rule), I decided not to collapse these items. None of the items 847 was significantly related to team performance. When added as control variables to the regression 848 analysis, the pattern of results did not change. 849 850 I n r e v i e w