The Banzhaf Power Index incorporates no information about producer behavior—it is simply a product of the voting rule and is not affected by the demand shift that will occur in the event the proposed action is passed. We thus use pre-vote outputs to calculate it. On the other hand, the Feasible Banzhaf Power Index uses the additional information about whether or not producers benefit from the MMO, so its value depends on the resulting shift in demand if the proposed action is passed. The formation voting rule that we consider requires at least two thirds of producers or producers of two thirds of output to vote for the MMO for it to be formed. Thus, there are two ways for a firm to be a critical voter. In Tables 2 and 3, we report the pre-vote market shares and Banzhaf Power Index and Feasible Banzhaf Power Index values associated with termination for the low cost firm and average high cost firm, respectively. The termination voting rule that we consider requires more than half of producers and producers of more than half of output to vote against the MMO for it to be terminated. Now, we return to our research question and examine how market power and cost heterogeneity affect voting power as measured by these two indices. In the case of formation, both the Banzhaf Power Index value and Feasible Banzhaf Power Index value of the low cost firm are highest under competition,square black flower bucket wholesale followed by the dominant firm/competitive fringe market structure and then the Cournot market structure. As the market power of the low cost firm increases, the low cost firm restricts its output relative to the competitive case to maintain a higher price.
Because the voting rule we consider is in part based on market share, this restriction of output causes the Banzhaf Power Index value to be smaller than it would be if the low cost firm did not have market power. This result holds under all cost advantages and can be seen in the first column labeled “BP” in Table 1 by comparing values for the three market structures for a given cost advantage. Changes in voting power are driven by three related factors: market share of the firm, the number of critical votes of the firm, and the probability of formation of coalitions in which the firm is critical. In all cases, the market share of the low cost firm increases as the low cost firm’s cost advantage increases. Finally, for the Feasible Banzhaf Power Index case, the probability of formation of coalitions in which the firm is critical weakly decreases for both types of firms as the low cost firm’s cost advantage increases.Across all three market structures in the case of MMO formation, we see that at low cost advantages the effect of increasing market share and the resulting increase in the number of critical votes dominate for the low cost firm. As market share of the low cost firm increases, coalitions that were not previously winning coalitions can become winning coalitions, and firms that are critical in these new winning coalitions see an increase in the number of critical votes. We see this phenomenon for high cost firms as well because even though their market share is decreasing, they benefit from the increase in winning coalitions. While the reason for this increase is logical for the low cost firm, it is less obvious for the high cost firm. This result is due to the particular nature of the voting rule; it is a union of two weighted voted games rather than an intersection. When the market shares of all the high cost firms are relatively similar to that of the low cost firm, the only winning coalitions will be those who contain many voters. Thus, the coalitions meeting one of the quotas will also meet the other quota. However, as the market share of the low cost firm increases, the number of coalitions that only meet one of the two quotas will increase, increasing the number of critical votes for both low and high cost firms.
This effect drives the Banzhaf Power Index value of all firms upward as the low cost firm’s cost advantage increases. The probability of coalitions forming is a product of the probabilities that the firms in the coalition will vote for the proposed action. The probability of winning coalitions forming increases if more firms benefit from the MMO. In the case of MMO formation, as the cost advantage of the low cost firm increases we see increasing heterogeneity and thus disagreement among the producers, which drives the probability of winning coalitions forming downward. In the dominant/competitive and competitive firm market structures in a vote for MMO formation, the critical vote effect dominates the probability effect at low cost advantages, but the market share of the low cost firm builds quickly and the probability effect begins to outweigh the critical vote effect. However, we see the opposite in the case of Cournot. At low cost advantages, the probability effect outweighs the critical vote effect. This is due to the fact that the market share of the low cost firm is relatively low at this point and increases very slowly, since all firms are acting strategically. Thus, the increase in the number of critical votes that occurs with an increase in market share and the number of winning coalitions is smaller than in the other two market structures. These result hold for both low cost and high cost producers. Comparing Feasible Banzhaf Power across demand shift scenarios, we see that for the dominant/competitive and competitive markets, both types of firms have weakly higher Feasible Banzhaf values with an inelastic demand shift compared to the other two types of shifts. This is due to the fact in the case of an inelastic demand shift, firms with low market share benefit more than those with high market share. In the case of Cournot, we see that the inelastic demand shift actually yields weakly lower Feasible Banzhaf Power as compared to the other two demand shifts across both firm types due to the smaller difference in market shares between the high and low cost firms. Although the determining factors are the same, the voting power results for MMO termination are different from those for formation. The three related factors driving changes in voting power are: market share of the firm, the number of critical votes of the firm, and the probability of formation of the coalition in which a firm is critical. In all cases, the market share of the low cost firm increases as the low cost firm’s cost advantage increases.
At the same time, the number of critical votes for the low cost firm increases as its cost advantage increases, but the number of critical votes for the high cost firms decrease, due to the nature of the voting rule as an intersection between two voting games, rather than a union like the formation rule. As the market share of low cost producers decreases,plastic square flower bucket winning coalitions that once met the production and number requirements of the voting rule may only meet the number requirement and therefore are no longer winning. This pattern of critical votes is reflected in the three columns of Banzhaf Power Index values in each of Tables 2 and 3, labeled “BP.” In looking at the Feasible Banzhaf Power Index, a first main difference to notice between Table 1 and Tables 2 and 3 is that the Feasible Banzhaf Power Index values in the latter two tables are an order of magnitude smaller. As indicated in the previous section, the probability of winning coalitions forming increases if more firms benefit from the MMO. We see relatively high values for Feasible Banzhaf Power for MMO formation as compared to MMO termination because more firms benefit from the MMO under the specified parameterization. Examining the probability of coalition formation, the probability of formation of coalitions in which the low cost firm is critical weakly decreases as its cost advantage increases across all three market structures and all three demand shifts. This result is consistent with disagreement among firms becoming more common as the market share of the low cost firm increases. However, in contrast to the MMO formation case, for the high cost firms in the dominant/competitive and competitive market structures, the probability of formation of coalitions in which they are critical first decreases as the low cost firm’s cost advantage increases, and then increases again at higher cost advantages. We again attribute this result to the more restrictive voting rule regarding termination. As the market share of the low cost firm increases, the market shares of the high cost firms necessarily decrease. Thus, at low cost advantages, as the cost advantage of the low cost firm increases, the winning coalitions in which the high cost firms are critical lose their ability to meet the production requirement of the voting rule and the winning coalitions that it remains in suffer from some disagreement. At higher cost advantages, as heterogeneity between the low cost and high cost producer increases, the high cost producers become critical in fewer winning coalitions due to this continued challenge of meeting the production requirement, but for those winning coalitions for which it is still critical, there is greater agreement among producers about the benefits of the MMO.
On the other hand, for the Cournot market structure, the number of critical votes decreases relatively slowly as cost advantage increases and the probability of coalition formation for the high cost producer decreases as well, so this effect seems to be driven by disagreement among producers as producer heterogeneity increases. However, despite these underlying differences across market structures, the net effect of these factors is that Feasible Banzhaf Power increases for the low cost firm as the low cost firm’s cost advantage increases, thus following the same pattern as the Banzhaf Power Index, as we see in Tables 2 and 3. There are no apparent differences in Feasible Banzhaf Power across demand shift scenarios. This result is not surprising and is consistent with the voting power literature. Since the voting rule requirements prevent a few large producers or many small producers from effecting change, shifts that yield disproportionate benefits are unlikely to afford producers greater Feasible Banzhaf Power. The consequences of plastic accumulation for marine organisms are well-documented and have received wide attention. Impacts of marine debris include transport of alien species and pollutants to new locations, smothering of sea floor biota, and sorption and toxicity of contaminants. Reports of entanglement and choking of marine wildlife are voluminous: more than 250 species are known to ingest or have been entangled in marine debris including seabirds, turtles, fish, crustaceans, and cetaceans, sometimes with documented consequences for fitness or population size. In contrast, impacts of debris on terrestrial organisms are poorly documented and have been largely ignored, perhaps because terrestrial debris is less conspicuous and more difficult to measure than marine debris. As was initially the case with marine wildlife, entangled and choking terrestrial wildlife might be difficult to detect without deliberate effort, and opportunistic observations may go unreported. Available data suggest that the impacts of debris on terrestrial organisms are similar to those on marine organisms, including sorption of chemicals and mortality linked to ingestion. Likewise, a number of studies report entanglement of terrestrial organisms, including snakes in beer can tabs, tortoises in balloon ribbon, and birds in anthropogenic nest material. Potential effects of debris on terrestrial organisms could be most substantial in intensively human-modified landscapes . One of the few previous studies of nest entanglement in terrestrial birds, for example, reported that 4.6% of Osprey nestlings in an agricultural setting were entangled in anthropogenic nest material . Likewise, urban settings are a primary source of trash entering marine and terrestrial protected areas. Historically, urban biotas have received very little attention, although interest has intensified in recent years in response to the rapid spread of urban landscapes across the earth’s surface. Nevertheless, the effects of plastic debris on urban organisms have been largely ignored. Impacts of debris could be magnified in urban adapted species, which are often characterized by their ability to utilize anthropogenic resources.