Wednesday, November 6, 2019

Our results suggest that individuals in a more positive mood are less likely to cooperate, and play less efficiently in a repeated Prisoner’s Dilemma

Happiness, cooperation and language. Eugenio Proto, Daniel Sgroi, Mahnaz Nazneen. Journal of Economic Behavior & Organization, November 6 2019.

Abstract: According to existing research across several disciplines (management, psychology, economics and neuroscience), positive mood can have positive effects, engendering more altruistic, open and helpful behaviour, but can also work through a more negative channel by inducing inward-orientation, assertiveness, and reduced use of information. This leaves the impact on cooperation in interactive and strategic situations unclear. We find evidence from 490 participants in a laboratory experiment suggesting that participants in an induced positive mood cooperate less in a repeated Prisoner’s Dilemma than participants in a neutral setting. This is robust to the number of repetitions or the inclusion of pre-play communication. In order to understand why positive mood might damage the propensity to cooperate, we conduct a language analysis of the pre-play communication between players. This analysis indicates that subjects in a more positive mood use more inward-oriented and more negative language.

Keywords: Positive moodAffectHappinessMood induction proceduresCooperationRepeated Prisoner’s DilemmaSocial preferencesSocial dilemmasCognitive skillsProductivityInward-orientationLanguage analysis

JEL classification: C72 (Cooperative games)C91 (Laboratory experiments)D91 (Role and effects of psychologicalemotionalsocialand cognitive factors on decision making)J24 (Productivity)J28 (Life satisfaction)

In a previous version:

5 Concluding Remarks

Our results suggest that individuals in a more positive mood are less likely to cooperate, and play less efficiently in a repeated Prisoner’s Dilemma. This supports what we described as the “negative channel” in the introduction, and suggests that this channel dominates the “positive channel” in a situation involving repeated play and strategic interaction. This is true both for the repeated Prisoner’s Dilemma with a known and unknown end date and for sessions both with and without pre-play communication. We also show that the result is not specific to a particular form of mood induction. The result holds right through to the final round of play, though it does not hold if we analyse only the very first round of each supergame.

A novel analysis of the text used in pre-play communication, to our knowledge the first of its kind in an economics laboratory experiment, suggests that those in a more positive mood use more negative language and display greater inward-orientation (through the greater use of the “I” pronoun) than those in a neutral mood which also supports the “negative channel”. We confirm that inward orientation is not specific to any one form of mood induction (it applies equally well to the use of movie clips or Velten statements and music) an our language analysis is. Our findings also support the concept of “mood maintenance” which explains why those with a higher level of happiness might shy away from the risks involved in cooperation: they have more to lose and less to gain compared to those at lower levels of happiness: this is most apparent when looking at the choice of defect where positive mood is associated with a 7.2 percentage point reduction (p-value 0.0232) in the cooperation. These findings are very different from results in the literature typically obtained in oneshot games or which do not involve strategic interaction. A simple explanation (supported by Proto et al. (2017)) is that repeated-interaction games involve more complex tasks where cognitive ability plays a crucial role.

Taken together with one of the key findings in the “negative channel” described earlier, that cognitive ability may be negatively related to positive mood, this might explain why subjects in a neutral mood are better equipped for more complex strategic settings. Finally, we should note that in our study we were specifically interested in the impact of general positive or neutral mood shocks and so elected to have everyone within a session face the same shock. Randomization then occurred across sessions not within sessions. This works well if we wish to consider a situation where everyone faces the same shock. Our work is not well-placed to study situations where individuals face different shocks and in judging how these might interact, for instance if one player has recently become happier while another has not. This is a potential topic for future study.

The rise in the political polarization in recent decades is not accounted for by the dramatic rise in internet use; claims that partisans inhabit wildly segregated echo chambers/filter bubbles are largely overstated

Deri, Sebastian. 2019. “Internet Use and Political Polarization: A Review.” PsyArXiv. November 6. doi:10.31234/

In this paper, I attempt to provide a comprehensive review of the evidence regarding the relationship between political polarization in the US and internet use. In the first part, I examine whether there has indeed been a rise in political polarization in the US in the last several decades. The remaining second and third parts deal with the relationship between polarization and internet use. I begin, in the second part, by reviewing evidence pertaining to the question of whether internet use plays a causal role in bringing about polarization. I then move, in the third part, to exploring the possible means by which internet use might bring about polarization. By analogy to cigarettes and cancer, the second part examines whether cigarette smoking causes cancer, while the third part examines how cigarette smoking causes (or might cause) cancer. One focus, in the third section, is on the most often discussed mechanism of internet-caused polarization: segregated information exposure, which corresponds to claims that polarization is been driven by an internet ecosystem characterized by “echo chambers”, “filter bubbles”, and otherwise partisan information consumption and dissemination.

The brief summary for each of the three parts is this. First, there is evidence that polarization has been on the rise in the U.S. in the recent decades—but it depends what you measure. When comparing Republican and Democrats, there is strongest evidence for increases in affective polarization and policy-based polarization. Second, most analyses would marshal against a version of reality where the rise in the political polarization in recent decades is mostly accounted for by the dramatic rise in internet use over this same time period. However, one notable, well-conducted, large-scale randomized direct intervention study confirms that de-activating a social media account (Facebook) resulted in significant and non-trivially sized decreases in polarization, specifically related to political opinions and policy preferences (Allcott, Braghieri, Eichmeyer, & Gentzkow, 2019). Finally, the evidence is murkiest regarding how internet use might drive polarization. With regard to polarization via segregated information exposure, claims that partisans inhabit wildly segregated “echo chambers” or “filter bubbles” are largely overstated. Nevertheless, there are significant and meaningful differences in the political content that partisans of different political orientations consume online, comparable to the degree of segregation in national print newspaper readership. Causal evidence linking this differential exposure to political polarization is not as strong as evidence that differential exposure exists. Evidence for other mechanisms of polarization is suggestive but awaits strong empirical confirmation.

Do exonerees face employment discrimination similar to actual offenders?

Do exonerees face employment discrimination similar to actual offenders? Jeff Kukucka, Heather K. Applegarth, Abby L. Mello. Legal and Criminological Psychology, November 6 2019.

Purpose: Given that criminal offenders face employment discrimination (Ahmed & Lang, 2017, IZA Journal of Labor Policy, 6) and wrongly convicted individuals are stereotyped similarly to offenders (Clow & Leach, 2015, Legal and Criminological Psychology, 20, 147), we tested the hypothesis that exonerees – despite their innocence – face employment discrimination comparable to actual offenders.

Methods: Experienced hiring professionals (N = 82) evaluated a job application that was identical apart from the applicant's criminal history (i.e., offender, exoneree, or none).

Results: As predicted, professionals formed more negative impressions of both the exoneree and offender – but unexpectedly, they stereotyped exonerees and offenders somewhat differently. Compared to the control applicant, professionals desired to contact more of the exoneree's references, and they offered the exoneree a lower wage.

Conclusions: Paradoxically, exonerees may be worse off than offenders to the extent that exonerees also face employment discrimination but have access to fewer resources. As the exoneree population continues to grow, research can and should inform policies and legislation in ways that will facilitate exonerees’ reintegration.


Our findings suggest that exonerees–despite their innocence–may face hiringdiscrimination similar to actual offenders. Compared to an applicant with no criminalhistory, hiring professionals formed less favourable impressions of exoneree and offenderapplicants, desired to contact more of the exoneree’s references, and were more likely tooffer the exoneree a low wage–all despite their applications being otherwise identical.Notably, the observed effects were consistent in magnitude with those seen in meta-analyses of race-based (Quillian, Pager, Hexel, & Midtbøen, 2017) and gender-based(Koch, D’Mello, & Sackett, 2015) hiring discrimination. For offenders, employment is animportant predictor of post-release adjustment (Bahr, Harris, Fisher, & Armstrong, 2010;Uggen, Wakefield, & Western, 2005), including lower recidivism. Similarly for exonerees,studies have found a positive relationship between employment and mental health(Wildemanet al., 2011) and a negative relationship between financial compensation andpost-release criminality (Mandery, Shlosberg, West, & Callaghan, 2013). Our findings thuscarry potentially broad implications for exonerees’ post-release well-being.

Like Clow and Leach (2015), we found that hiring professionals negatively stereotypedboth offenders and exonerees–but we also unexpectedly found some evidence that theywere stereotyped differently. While both were seen as less trustworthy than the controlapplicant, exonerees were generally seen as intellectually deficient (i.e., less intelligent,competent, and articulate), whereas offenders were generally seen asmotivationallydeficient (i.e., less conscientious and responsible). If that is the case, then discrimination against these populations may depend on the requirements of the job in question. In our study, applicants sought a job that required both intellect and leadership, which may have made exonerees and offenders equally undesirable candidates. Still, this finding is rather tentative; future research should more carefully explore the possibility that these populations are stereotyped differently and therefore face discrimination under different circumstances.

The tendency to stereotype exonerees as unintelligent suggests that professionals may have attributed the exoneree’s conviction to dispositional rather than situational factors (Gilbert & Malone, 1995; Ross, 1977). Just world theory–which posits that people have afundamental need to view the world as fair (Hafer & B egue, 2005; Lerner & Miller, 1978)–may shed light on why exonerees would be blamed for their own plight: When faced withinjustice, people preserve their belief in a just worldby blaming the victim. In turn, peopleare less helpful to those who appear responsible for their own plight (Farwell & Weiner,2000; Weiner, Perry, & Magnusson, 1988)–and indeed, recent work has found that blaming exonerees for their own conviction predicted lower support for post-exoneration services (Kukucka & Evelo, 2019; Scherr, Normile, & Putney, 2018). This literature may thus explain why professionals stereotyped exonerees as unintelligent and why they more often offered exonerees a low wage. Perhaps educating employers about thesystemic causes of wrongful conviction would reduce discrimination against exonerees. Consistent with this possibility, Ricciardelli and Clow (2012) found that students’attitudes towards exonerees became more positive after hearing a lecture on the causes ofwrongful conviction.

Our professionals also wanted to contact more of the exoneree’s references, and they were equally likely to cite criminal history as a negative quality of the exoneree andoffender. These findings may indicate that professionals doubted the exoneree’s innocence. Qualitative studies abound with examples of exonerees who the publicpresumed guilty even after their exoneration (Scott, 2010; Westervelt & Cook, 2010), andother findings suggest that laypeople are often unconvinced of exonerees’ innocence(Scherr, Normile, & Sarmiento, 2018). If our professionals felt similarly, then it isunsurprising that they were equally apprehensive about the exoneree’s and offender’scriminal history. Alternatively, professionals may have accepted the exoneree’sinnocence but feared that incarceration had tainted them. This possibility is consistentwith research on stigma by association as well as the ‘magical law of contagion’–that is,the belief that people take on the properties of others with whom they have contact (e.g.,Rozin & Royzman, 2001). In other words, people may believe that exonerees take on thesame traits as the offenders with whom they cohabitated in prison (Clowet al., 2012). Future research should explore whether exonerees are stigmatized because they are mistakenly thought to be offenders or because they are known to have cohabitated with offenders.

Amazing how much we may hate the others — The Harmful Side of Thanks: Thankful Responses to High-Power Group Help Undermine Low-Power Groups’ Protest, Pacifying Them

Amazing how much we may hate the others — The Harmful Side of Thanks: Thankful Responses to High-Power Group Help Undermine Low-Power Groups’ Protest. Inna Ksenofontov, Julia C. Becker. Personality and Social Psychology Bulletin, October 9, 2019.

Abstract: Giving thanks has multiple psychological benefits. However, within intergroup contexts, thankful responses from low-power to high-power group members could solidify the power hierarchy. The other-oriented nature of grateful expressions could mask power differences and discourage low-power group members from advocating for their ingroup interests. In five studies (N = 825), we examine the novel idea of a potentially harmful side of “thanks,” using correlational and experimental designs and a follow-up. Across different contexts, expressing thanks to a high-power group member who transgressed and then helped undermined low-power group members’ protest intentions and actual protest. Thus, the expression of thanks can pacify members of low-power groups. We offer insights into the underlying process by showing that forgiveness of the high-power benefactor and system justification mediate this effect. Our findings provide evidence for a problematic side of gratitude within intergroup relations. We discuss social implications.

Keywords: expressions of thanks, protest, intergroup helping, system justification, forgiveness

How can you thank a man for giving you what’s already yours? How then can you thank him for giving you only part of what’s already yours?
             —Malcolm X, “The Ballot or the Bullet,” 1964

Mild alcohol use is shown to improve bargaining efficiency in labs; the effect does not arise from changes in mood, altruism, or risk aversion; may be caused by impairment in information processing ability, diminishing self-interest

From 2016... Deal or no deal? The effect of alcohol drinking on bargaining. Pak HungAu, Jipeng Zhang. Journal of Economic Behavior & Organization, Volume 127, July 2016, Pages 70-86.

•    Mild alcohol use is shown to improve bargaining efficiency in experiments.
•    The effect does not arise from changes in mood, altruism, or risk aversion.
•    The effect can be caused by impairment in information processing ability.

Abstract: Alcohol drinking during business negotiation is a very common practice, particularly in some East Asian countries. Does alcohol consumption affect negotiator's strategy and consequently the outcome of the negotiation? If so, what is the mechanism through which alcohol impacts negotiator's behavior? We investigate the effect of a moderate amount of alcohol on negotiation using controlled experiments. Subjects are randomly matched into pairs to play a bargaining game with adverse selection. In the game, each subject is given a private endowment. The total endowment is scaled up and shared equally between the pair provided that they agree to collaborate. It is found that a moderate amount of alcohol consumption increases subjects’ willingness to collaborate, thus improving their average payoff. We find that alcohol consumption increases neither subjects’ preference for risk nor altruism. A possible explanation for the increase in the likelihood of collaboration is that subjects under the influence of alcohol are more “cursed” in the sense of Eyster and Rabin (2005), which is supported by the estimation results of a structural model of quantal response equilibrium.

5. Concluding remarks

Given the harmful effects of excessive alcohol consumption on health are well-known, it is not clear and thereforeinteresting to investigate why aggressive business drinking has become a routine, and even an accepted culture in manycountries. In this study, we make the first attempt to study the effect of a mild amount of alcohol consumption on bargainingunder incomplete information. We find a positive effect of alcohol consumption on the efficiency of bargaining in a specificexperimental setting. Our finding suggests that consuming a mild to moderate amount of alcoholic drink in business meetings can potentially help smooth the negotiation process.

Out of the concern of health risk, the alcohol consumption of subjects in our experiment is mild relative to businessdrinking in real world. Our results still can shed useful light on understanding the effect of business drinking. First, thea lcohol intoxication effects, especially on information processing and working memory, have shown to be present even at amild dose of alcohol similar to that used in our experiment (Dry et al., 2012). Moreover, the intoxication effect is increasingin BAC up to a moderate level. We thus conjecture that a slight increase in dosage would strengthen our results. Second,the medical literature has well documented that chronic alcohol consumption makes the drinker develop tolerance to someof alcohol’s effects.20Consequently, the amount of alcohol needed to achieve a certain level of intoxication for a graduatestudent (who do not drink much typically) can be much smaller than the amount for a businessman (who drinks moreheavily and frequently).

Despite the aforementioned positive effect for a mild dose of alcohol, caution must be exercised in extrapolating theresults too far. It is well known that an excessive dose of alcohol can lead to a range of harmful effects, including aggressiveand violent behaviors (Dougherty et al., 1999), as well as impairment in problem solving ability (Streufert et al., 1993). Therefore, it is almost certain that excessive drinking would hamper efficiency in bargaining.

What are the channels through which alcohol use affects bargaining strategies and outcomes in our setting? It is commonly accepted that alcohol use lowers one’s ability to make appropriate reasoning and inference from available information. Therefore, in settings in which skepticism can lead to a breakdown in negotiation, alcohol consumption can make people drop their guard for each others’ actions, thus facilitating reaching an agreement. Our QRE estimation of a cursed equilibrium provides some support for this channel.

Other conceivable channels can be ruled out as follows. First, in line with the existing literature on the effect of alcoholuse, we find that a mild does of alcohol has little (if not zero) effect on our subjects’ risk aversion and altruism. Therefore,the increase in willingness to collaborate does not arise from a decrease in risk aversion, and/or an increase in altruism.

Second, the positive effect of alcohol in social setting has often been attributed to creating a more comforting and relaxingatmosphere. Our experiment is conducted in a laboratory, and each subject consumed the given beer individually. As such,the socializing effect of alcohol is clearly absent in our setting. Third, alcohol consumption has been suggested to have asignaling value that one is trustworthy and is ready to commit to a relationship. (See for example, Haucap and Herr (2014)and Schweitzer and Kerr (2000).) In our study, treatments are randomized and enforced by the experimenters: subjects donot get to choose whether and what type of drink to consume, so they cannot signal their private information. Whereas ourexperiment design abstracts away from the second and the third channels discussed above, future research can consideralcohol’s effects on relieving tension and building trust in a social setting.

Thank God for My Successes (Not My Failures): Feeling God’s Presence Explains a God Attribution Bias

Thank God for My Successes (Not My Failures): Feeling God’s Presence Explains a God Attribution Bias. Amber DeBono, Dennis Poepsel, Natarshia Corley. Psychological Reports, November 4, 2019.

Abstract: Little research has investigated attributional biases to God for positive and negative personal events. Consistent with past work, we predicted that people who believe in God will attribute successes more to God than failures, particularly for highly religious people. We also predicted that believing that God is a part of the self would increase how much people felt God’s presence which would result in giving God more credit for successes. Our study (N = 133) was a two-factor, between-subject experimental design in which participants either won or lost a game and were asked to attribute the cause of this outcome to themselves, God, or other factors. Furthermore, participants either completed the game before or after responding to questions about their religious beliefs. Overall, there was support for our predictions. Our results have important implications for attribution research and the practical psychological experiences for religious people making attributions for their successes and failures.

Keywords: Religion, God, attribution, self


The results of this study provided substantial evidence for our two primarygoals. First, we demonstrated that people who believe in God attributed successes more to God than their failures. Furthermore, we showed that thiseffect was stronger for people who identified as more religious. We thereforeconceptually replicated previous research (Spilka & Schmidt, 1983), demonstrating that this God attribution style is a reliable effect, not limited to hypo-thetical scenarios.

Moreover, the percentage attributed to God for a win appeared to be bestpredicted by believing God is a part of them. This relationship was bestexplained by simply feeling God’s presence during the experimental task.These findings are consistent with previous research that showed the importanceof the overlap between God and self in addition to feeling God’s presence (e.g.,Hodges et al., 2013; Sharp et al., 2017). In contrast with Spilka and Schmidt’s(1983) findings, our results indicated that the overlap between God and the selfmay provide a better explanation than religious commitment for how peopleattribute successes to God, by feeling God’s presence. Our review of the literature suggests this may be the first study to investigate these concepts as explan-ations for differing attribution styles for failures and successes.

Strengths  and  implications

Until now, little research has investigated why and how God-believers attributetheir successes to God more than their failures. We replicated the results of a setof over 30-year-old studies (Spilka & Schmidt, 1983). Contrary to these originalstudies, our research did not use hypothetical events; our participants experienced real-life successes and failures. Despite this seemingly stable effect, little research has explained why people who believe in God experienced a God attri-bution bias instead of a self-serving bias. We again showed that a God attribution bias may be a result of religious commitment. In addition to conceptually replicating these over 30-year-old findings (which is important in and of itself), we also found evidence for some possible mechanisms to explain this God attri-bution bias. That is, believing God is a part of them, a variable potentially moreimportant than religiosity, appeared to increase feeling God’s presence whichresulted in greater attributions to God for successes. This is the first setof studies that show these beliefs may play an important role in the God attribution bias.

These results also indicate that a more nuanced approach is needed to under-stand why people attribute successes more to God than failures and how thisimpacts people’s thinking and behavior. Although vignettes are better thansimple survey measures (Alexander & Becker, 1978), they are problematic aspeople might believe they would make attributions one way when in reality theymay do another (Barter & Renold, 1999). Our study is the first to examine God attributional styles for actual experiences of failures and successes by the participants. Nevertheless, the results of our study were consistent with the vignetteresearch: while religious individuals were more likely to use this God-serving attributional style, we saw that people generally tended to give God more credit for successes than failures. We also found support for the idea that feeling Godas a part of the self, which resulted in feeling God’s presence also predictedgiving God greater credit, but only for successes. Religious commitment did notexplain this effect as well as feeling God is a part of the self.

Although the Battleship game held little consequences for participants(whether they won or lost resulted in no benefit or penalty), even with thisinconsequential task, we saw that people will attribute successes more to Godand failures to themselves. Yet, the successes and failures in life often result inreal consequences. Our study showed that even inconsequential failures andsuccesses can lead to God attributional biases seen in previous research. Thus,we would predict a similar God attributional pattern between both consequen-tial and inconsequential tasks, inside and outside of the laboratory.

Our results also suggest that people who are especially religious may be morelikely to attribute their successes more to God than their failures. People whouse this attributional style should be more mindful of these attribution tenden-cies, as giving God credit for successes and taking credit for failures could resultin depression. Potentially, this could explain slumps we see in highly religiousathletes. If athletes give credit to God for successes on the field, this may appearas humility to some, but this type of thinking could quickly lead to the samedownward spiral thinking that we see in people suffering from depression (Alloy& Abramson, 1988). It would be prudent for all of us, especially for people whobelieve in God, to be aware of how much credit we are taking for our successesand failures. As such, Sports Psychologists may consider heeding this line ofthinking in their religious athletes, so that they can break out of their “slumps.”

Our findings also further our understanding of SIT, by showing that religiousidentity may be less important for explaining attributions to God for successesthan experiencing God as part of the self. Although religiosity, an aspect ofone’s collective identity, moderated the effect of wins on attributions to God,experiencing God as part of the self predicted feeling God’s presence, which thenpredicted attributing the win to God. Religious commitment did not explain thiseffect as well. Future research should continue to examine these two variables,religiosity and experiencing God as part of the self, when attempting to explainattributional styles.

On the Mathematics of the Fraternal Birth Order Effect and the Genetics of Homosexuality

On the Mathematics of the Fraternal Birth Order Effect and the Genetics of Homosexuality. Tanya Khovanova. Archives of Sexual Behavior, November 5 2019.

Abstract: Mathematicians have always been attracted to the field of genetics. The mathematical aspects of research on homosexuality are especially interesting. Certain studies show that male homosexuality may have a genetic component that is correlated with female fertility. Other studies show the existence of the fraternal birth order effect, that is, the correlation of homosexuality with the number of older brothers. This article is devoted to the mathematical aspects of how these two phenomena are interconnected. In particular, we show that the fraternal birth order effect implies a correlation between homosexuality and maternal fecundity. Vice versa, we show that the correlation between homosexuality and female fecundity implies the increase in the probability of the younger brothers being homosexual.

Keywords: Fraternal birth order effect Male homosexuality Fecundity Genetics Sexual orientation


According to the study by Blanchard and Bogaert (1996): “[E]ach additional older brother increased the odds of [male] homosexuality by 34% ” (see also Blanchard [2004], Bogaert [2006], Bogaert  et al. [2018], and a recent survey by Blan-chard [2018]). The current explanation is that carrying a boy to term changes their mother’s uterine environment. Male fetuses produce H–Y antigens which may be responsible for this environmental change for future fetuses.

The research into a genetic component of male gayness shows that there might be some genes in the X chromosome that influence male homosexuality. It also shows that the same genes might be responsible for increased fertility in females (see Ciani, Cermelli, & Zanzotto [2008] and Iemmola & Ciani [2009]).

In this article, we compare two mathematical models. In these mathematical models, we disregard girls for the sake of clarity and simplicity.

The first mathematical model of the Fraternal Birth Order Effect (FBOE), which we denote FBOE-model, assumes that each next-born son becomes homosexual with increased probability. This probability is independent of any other factor.

The second mathematical model of Female Fecundity (FF), which we denote FF-model, assumes that a son becomes homosexual with probability depending on the total number of chil-dren and nothing else.

We show mathematically how FBOE-model implies correlation with family size and FF-model implies correlation with birth order. That means these two models are math-ematically intertwined.We also propose the Brother Effect. Brothers share a lot of the same genes. It is not surprising that brothers are more probable to share traits. With respect to homosexuality, we call the correlation that homosexuals are more probable to have a homosexual brother than a non-homosexual the Brother Effect. The existence of genes that increase predisposition to homo-sexuality implies the Brother Effect. The connection between the FBOE-model and the Brother Effect is more complicated.

We also discuss how to separate FBOE and FF in the data.

The “Extreme Examples” section contains  extreme mathematical examples that amplify the results of this article. The “FBOE-model and the family size” section shows how FBOE-model implies the correlation with family size. The “FF-model implies birth order correlation” section shows how FF-model implies the correlation with birth order. In the “Brothers” section, we discuss the connection between FBOE-model and the Brother Effect. In the “Separating Birth Order and Female Fecundity” section, we discuss how to separate the birth order from the family size.