We develop several $\ell ^p$-operator norm inequalities for $k\times k$ block matrices defined on the $\ell ^p$-sum of Banach spaces. Using these inequalities, we obtain p-numerical radius and spectral radius bounds for $k\times k$ block matrices. We deduce a p-numerical radius bound for the Kronecker product $A\otimes B$, where $A\in {M}_k(\mathbb {C})$ is a $k\times k$ complex matrix and $B\in \mathcal {L}(\mathbb {H})$ is a bounded linear operator on a complex Hilbert space $\mathbb {H}$. This improves and extends Holbrook’s bound $w(A\otimes B)\leq w(A)\|B\|.$ If $\|A\|_{\ell ^p}$ and $w_p(A)$ denote the $\ell ^p$-operator norm and p-numerical radius of $A\in {M}_k(\mathbb {C})$, respectively, then it is shown that

$$ \begin{align*} \frac{1}{2}\|A\|_p+\mu_p(A) \leq w_p(A), \end{align*} $$

$\mu _p(A)$

$\ell ^p$

$\frac {1}{2}\|A\|_p= w_p(A)$

This study deploys netnography to investigate online reaction to suzhi jiaoyu, China’s national curriculum. Few papers have attempted to gauge popular opinion on the curriculum, despite state rhetoric that, once universally implemented, it will revolutionize China’s development. I analyse 1,644 posts of netizens’ judgements of ongoing suzhi jiaoyu reforms, uploaded to China’s most popular “question-and-answer” site, Zhihu. Deploying grounded theory to gauge the levels and nature of consensus/dissent across opinions, my study details the unpopularity of suzhi jiaoyu among users of Zhihu. Most appropriate suzhi jiaoyu discourse to criticize China’s unequal distribution of resources and, implicitly, the failure of state initiatives to address these inequalities. Users perceive the previous national curriculum to be fairer, noting the absence of sufficient state intervention in this area. I conclude by examining the broader implications of Zhihu users’ engagement with social problems in China.

Drawing upon a large longitudinal qualitative study on lived experiences of food aid in England, we question contemporary academic and policy categorisations and portrayals of food aid. Contrary to ideas of a diverse food aid sector offering choice and dignity, we identify clear uniformity in the language participants use to describe different forms of food charity; any organisation which offers food for free or at very low cost to take away is predominantly described as a ‘food bank’. Simultaneously, however, we find marked inequalities in lived experiences of food charity by gender, age and race and ethnicity, and clear indications that demographically oriented exclusion is ever-present in food aid. We argue that the key fault line shaping lived experiences of the UK community food sector is not the ‘type’ of provision but demography (age, gender and parenthood, race and ethnicity) and yet inequalities remain broadly ignored in discussions of UK food aid. In doing so, we provide a critical contribution to scholarship on the changing nature of welfare pluralism and the lived experience of poverty today.

The question of how digital health is regulated has become increasingly important within debates on technology, inequality and global health. While digital health is frequently celebrated for its capacity to expand access, build resilient systems and advance equity, scholars have raised critical concerns about its role in reproducing asymmetries of power. The potential for reproducing rather than curbing inequality is particularly relevant for the Global South. This Special Issue of the International Journal of Law in Context interrogates the ways in which digital health infrastructures, regulatory frameworks and transnational data flows are constitutive of coloniality and neoliberal capitalism. Bringing together socio-legal, feminist and decolonial perspectives, the contributions examine regulation as a terrain in which vulnerabilities, exclusions and structural inequalities are reinforced. Against the celebratory rhetoric of innovation, this collection situates regulation as a key site for understanding the entanglement of digital health with broader histories of coloniality and capitalism.

Education plays an important role in the political, social and economic divisions that have recently characterised Western Europe. Despite the many analyses of education and its political consequences, however, previous research has not investigated whether government policy caters more to the preferences of the higher educated than to the preferences of the lower educated. We address this question using an original dataset of public opinion and government policy in the Netherlands. This data reveals that policy representation is starkly unequal. The association between support for policy change and actual change is much stronger for highly educated citizens than for low and middle educated citizens, and only the highly educated appear to have any independent influence on policy. This inequality extends to the economic and cultural dimensions of political competition. Our findings have major implications for the educational divide in Western Europe, as they reflect both a consequence and cause of this divide.

Political responsiveness is highly unequal along class lines, which has triggered a lively debate about potential causes of this political inequality. What has remained largely unexplored in this debate are the structural economic conditions under which policymakers operate. In this contribution, we hypothesize that budgetary pressures affect both the level and the equality of political responsiveness. Using a dataset containing public opinion data on around 450 fiscal policy proposals in Germany between 1980 and 2016, we investigate whether policymakers are more responsive on issues with budgetary consequences under conditions of low fiscal pressure than under conditions of high fiscal pressure. We find that responsiveness indeed varies systematically with the degree of fiscal pressure and that policymakers are less responsive on fiscal issues when fiscal pressure is high. This holds for both left‐wing and right‐wing governments. In contrast, we do not find strong effects of fiscal pressure on political inequality: responsiveness is not more equal in fiscally more permissive times. However, since different types of policy proposals are adopted in times of high fiscal stress, unequal responsiveness has different policy implications in times of high and low fiscal pressure.

This paper explores a major road to substantive representation in democracies, by clarifying whether demands of rich and poor citizens are taken up in the electoral platforms of political parties. Doing so constitutes a substantial broadening and deepening of our understanding of substantive representation – broadening the countries, issue‐areas and years that form the empirical basis for judging whether democracies manifest unequal representation; and deepening the process of representation by clarifying a key pathway connecting societal demands to policy outcomes. The paper hypothesises that party systems in general will respond more strongly to wealthy than to poor segments of a polity. It also hypothesises that left parties will more faithfully represent poorer and less significantly represent richer citizens than do right parties. We find substantial support for these expectations in a new dataset that combines multi‐country, multi‐issue‐area, multi‐wave survey data with data on party platforms for 39 democracies.

In recent years, scholars have observed that political parties’ policy positions frequently fit the preferences of well‐to‐do voters better than those of the less well‐to‐do; a phenomenon known as policy congruence inequality. While the existence of inequality in policy congruence is well‐established, we currently only have a modest understanding of the causes of it. We develop an argument proposing that the political mobilisation of citizens with low socioeconomic status (SES) both in the parliamentary channel, in the form of high turnout, and in the extra‐parliamentary channel, in the form of high union density, is pivotal. Both high turnout and union density force parties to pay more attention to the preferences of the disadvantaged, thereby creating lower policy congruence inequality. To test the argument, we have collected and harmonised election surveys and party manifestos covering 90 elections in Australia, Denmark, Germany, Sweden, Switzerland, the United Kingdom and the United States, covering several decades until today, yielding more than 120,000 voter–party dyads. Employing this new dataset, our results confirm that the political mobilisation of citizens with low SES is a strong predictor of policy congruence inequality. This finding nuances the conclusion of extant research by showing that low‐SES citizens are not always on the losing side politically. It also implies the important role of maintaining or maybe even increasing turnout and union membership among the disadvantaged in society. Places where either turnout or union density is slipping in these years are likely to witness further increases in policy congruence inequality in the years to come.

Inequality is a central explanation of political distrust in democracies, but has so far rarely been considered a cause of (dis‐)trust towards supranational governance. Moreover, while political scientists have extensively engaged with income inequality, other salient forms of inequality, such as the regional wealth distribution, have been sidelined. These issues point to a more general shortcoming in the literature. Determinants of trust in national and European institutions are often theorized independently, even though empirical studies have demonstrated large interdependence in citizens’ evaluations of national and supranational governance levels. In this paper, we argue that inequality has two salient dimensions: (1) income inequality and (2) regional inequality. Both dimensions are important antecedent causes of European Union (EU) trust, the effects of which are mediated by evaluations of national institutions. On the micro‐level, we suggest that inequality decreases a person's trust in national institutions and thereby diminishes the positive effect of national trust on EU trust. On the macro‐level, inequality decreases country averages of trust in national institutions. This, however, informs an individual's trust in the EU positively, compensating for the seemingly untrustworthiness of national institutions. Finally, we propose that residing in an economically declining region can depress institutional trust. We find empirical support for our arguments by analysing regional temporal change over four waves of the European Social Survey 2010–2016 with a sample of 209 regions nested in 24 EU member states. We show that changes in a member state's regional inequality have similarly strong effects on trust as changes in the Gini coefficient of income inequality. Applying causal mediation techniques, we can show that the effects of inequality on EU trust are largely mediated through citizens’ evaluations of national institutions. In contrast, residing in an economically declining region directly depresses EU trust, with economically lagging areas turning their back on European governance and resorting to the national level instead. Our findings highlight the relevance of regional inequality for refining our understanding of citizens’ support for Europe's multi‐level governance system and the advantages of causal modelling for the analysis of political preferences in a multi‐level governance system.

Stringent policies that significantly increase the cost of greenhouse gas emissions, such as CO${}_2$$_2$, are increasingly necessary for mitigating climate change. Yet while richer individuals in society generate the most CO${}_2$$_2$ emissions and thus will face the largest absolute cost burden, they also tend to be more supportive of stringent environmental policies. In this paper, we examine how information about the distribution of carbon emissions by income affects support for carbon taxation. While carbon taxation is widely advocated as the most efficient policy for mitigating climate change, it faces significant political hurdles due to its distributional costs. Using original survey data, with an embedded experiment, we find that providing information about the actual distribution of household CO${}_2$$_2$ emissions by income significantly changes individuals' support for carbon taxation. These effects are particularly pronounced at the bottom of the household income distribution, leading to increased support for costly climate policies. However, individuals who believe that carbon taxes will reduce their income continue to hold their level of support for carbon taxation. Our findings have significant implications for understanding the public's response to the distributional consequences of the green transitions and ultimately their political feasibility.

Have concerns about equal rights and equal chances crowded out economic equality as a priority of left parties? Despite the increased importance of inequality in political science, this contentiously fought debate has been standing on shaky empirical foundations. While voter's equality preferences are well understood, parties’ equality emphases remain uncharted territory. This research note assesses whether the Left has replaced its emphasis on economic equality with a focus on equal chances and equal rights. Based on a new dataset of 300,000 party statements, we use online crowd‐coding to map the equality trajectories of left parties in 12 OECD countries from 1970 to 2020. We examine if trade‐offs between economic and non‐economic aspects of inequality have come to dominate left parties’ equality profiles. Distinguishing social democratic, green and far‐left parties, we refute a meritocratic or ‘woke’ crowding out of redistribution. Yet, Social Democrats have indeed forsaken the once complementary link between economic equality and equal rights in favour of a weak trade‐off.

Features of electoral systems have been found to have positive effects on evaluations of democracy. This article proposes that there are larger social forces that must be accounted for in such analyses. Using European Social Survey measures of democratic expectations and the ‘satisfaction with democracy’ item, this study tests for effects of electoral rules on perceptions of democracy. It is found that multipartyism/proportionality and preferential ballot structure appear to correspond with positive evaluations of elections and parties, and with greater satisfaction with how democracy is functioning. However, these relationships dissipate when corruption and income inequality are accounted for. This suggests substantial limits to the capacity of electoral reforms to enhance democratic legitimacy. It also suggests that studies of mass perceptions of democratic performance may over‐estimate effects of electoral rules if country‐level corruption and income inequality are not accounted for.

How do people perceive the utility of redistribution? Support for redistribution is commonly understood as being determined by self‐interest in a way that is monotonically proportional to expected net transfers. However, this would imply that average support for redistribution is static and unaffected by changes in the distribution of incomes. This study addresses this incongruence by integrating concepts from the literature on redistribution preferences, namely the diminishing marginal utility of income, inequity aversion and loss aversion. These concepts are formalized by making two distinctions regarding redistribution: absolute versus relative utility and gains versus losses. An analysis of the European/World Values Survey suggests that the preferences of the poor are determined by absolute gains, while the preferences of the rich are determined by relative losses. In other words, the poor care about how much they gain from redistribution, while the rich care about the share of their income that they lose from it. The findings have important implications for the relationships among public opinion, economic development and income inequality.

For a number of Western democracies, it has been observed that the preferences of poor and rich citizens are unequally represented in political institutions and outcomes. Yet, the causes of this phenomenon are still under debate. We focus on the role of elections in this process, by disentangling biases towards different income groups that stem from the party system and from voters’ behaviour. Our aim is to uncover whether elections as selection mechanisms contribute to unequal representation by analysing factors of the supply and demand sides of the electoral process. On the supply side, we focus on the congruence of parties’ policy offers and voters’ preference distributions. This shapes citizens’ possibilities to express their policy preferences. On the demand side, we are interested in the extent to which citizens from different income groups base their vote decisions on their policy preferences. The empirical analysis relies on the European Social Survey and the Chapel Hill Expert Survey and covers 13 Western European countries. Our results indicate, first, that the economic and cultural preferences of poor and rich citizens differ significantly, and second, that party systems in the countries under investigation represent the lowest income groups the worst, and the middle income groups the best. This makes it difficult for citizens at both the lower and the higher end of the income distribution to voice their preferences in elections. Additionally, we show that low income citizens tend to take policy less into consideration when making an electoral choice than richer citizens. Thus, while the rich make up for their representation bias by taking policy more into account in their voting behaviour, the electoral stage poses another obstacle for the poor to overcome the representation bias. In summary it can be said that already on the supply side there is an unbalanced disadvantage in terms of representation for the very poor and the very rich, but the pattern leads to an even more asymmetrical misrepresentation of the poor due to the election act.

Seminal models in political economy imply that rising economic inequality should lead to growing public demand for redistribution. Yet, existing empirical evidence on this link is both limited and inconclusive – and scholars regularly doubt it exists at all. In this research note, we turn to data from the International Social Survey Programme's (ISSP) Social Inequality surveys, now spanning the period from 1987 to 2019, to reassess the effect of rising inequality on support for redistribution. Covering a longer time series than previous studies, we obtain robust evidence that when income inequality rises in a country, public support for income redistribution tends to go up. Examining the reaction across income groups to adjudicate between different models of how rising inequality matters in a second step, we find that rising inequality increases support for redistribution within all income groups, with a marginally stronger effect among the well‐off. Our results imply that insufficient policy responses to rising inequality may be less about absent demand and more about a failure to turn demand into policy, and that scholars should devote more attention to the latter.