The paradox of grading systems

We distinguish between (i) voting systems in which voters can rank candidates and (ii) those in which they can grade candidates, using two or more grades. In approval voting, voters can assign two grades only—approve (1) or not approve (0)—to candidates. While two grades rule out a discrepancy between the average-grade winners, who receive the highest average grade, and the superior-grade winners, who receive more superior grades in pairwise comparisons (akin to Condorcet winners), more than two grades allow it. We call this discrepancy between the two kinds of winners the paradox of grading systems, which we illustrate with several examples and whose probability we estimate for sincere and strategic voters through a Monte Carlo simulation. We discuss the tradeoff between (i) allowing more than two grades, but risking the paradox, and (ii) precluding the paradox, but restricting voters to two grades.     

The Relationship Between School Engagement and Delinquency in Late Childhood and Early Adolescence

Engagement in school is crucial for academic success and school completion. Surprisingly little research has focused on the relationship between student engagement and delinquency. This study examines whether engagement predicts subsequent school and general misconduct among 4,890 inner-city Chicago elementary school students (mean age: 11 years and 4 months; 43.3% boys; 66.5% black; 28.8% Latino). To improve upon prior research in this area, we distinguish three types of engagement (emotional, behavioral, and cognitive), examine whether the relationship between engagement and misconduct is bidirectional (misconduct also impairs engagement), and control for possible common causes of low engagement and misconduct, including peer and family relationships and relatively stable indicators of risk-proneness. Emotional and behavioral engagement predict decreases in school and general delinquency. However, cognitive engagement is associated with increases in these outcomes. School and general delinquency predict decreased engagement only in the cognitive domain. Suggestions for future research and implications for policy are discussed.