Too old to vote? A democratic analysis of age-weighted voting

Are there any prima facie reasons that democracies might have for disenfranchising older citizens? This question reflects increasingly salient, but often incompletely theorized complaints that members of democratic publics advance about older citizens’ electoral influence. Rather than rejecting these complaints out of hand, we explore whether, suitably reconstructed, they withstand democratic scrutiny. More specifically, we examine whether the account of political equality that seems to most fittingly capture the logic of these complaints – namely, equal opportunity of political influence over electoral outcomes – can justify disenfranchising older citizens. We conclude that equal opportunity of influence cannot ground a blanket disenfranchisement of older people and that, taken in conjunction with other general considerations that apply to all sound electoral policies, partial disenfranchisement proposals (i.e. proposals for reducing the electoral influence of older citizens via age-weighted voting) are both quasi-inapplicable and practically unrobust across a relevant range of political contexts.

do so. People 65 and older, for example, are more than three times as likely to make political donations as those under 30. As a result, their voices, amplified by money, carry farther politically than those of the young and impecunious. There are a lot of voices in their chorus. The American electorate is the oldest it's been since at least 1970 and is graying at a rapid clip, with the well-off living longer than ever before." 1 2. In a 2017 letter to The Independent, Geoffrey Downs writes that "It's all very well relatively well-off over-65 s being prepared to accept Brexit economic damagethey won't live with the consequences for as long as younger people, or feel them as much. Clearly, they skewed the Brexit referendum result. The answer is simple: give the vote to people at 16 for both elections and referenda (…) and take it away from them at retirement age." 2 These complaints point to an argument that supporters of representative democracies might consider endorsing. The argument is that older citizens can exert an unjustifiably disproportionate amount of electoral influence, as compared to less old (albeit not necessarily young) citizens. Granting older citizens equal voting rights might thus fail to satisfy one of the central standards of democracynamely, political equality. This may strike us as counterintuitive, since political equality normally calls for equal voting rights. But, at least under one interpretation that we examine below, political equality does not seem to always hold among those who, when granted equal voting rights, can gain unjustifiably unequal political sway. 3 In what follows, we conditionally take equal opportunity of political influence as one plausible view about political equality. As discussed below, this is not to deny that there are other, perhaps ultimately sounder strategies for formulating the demands of political equality. Rather, our aim is to focus on an understanding of political equality that most fittingly and charitably captures the logic of the complaints raised against the disproportionate electoral influence of older citizens, and thus offers their strongest principled defense.
To anticipate, our conclusion is that radical proposals for a blanket disenfranchisement of older citizens fail for equal influence reasons alone, and that more modest proposals for partially disenfranchising older citizensi.e., for reducing their electoral weightfail for equal influence reasons in conjunction with other general considerations that apply to all electoral policies, irrespective of their normative premises. In particular, we show that there are significant epistemic limitations to deciding the size of age-relative electoral weights and that equal influence might, under some realistic circumstances, require increasing older citizens' voting weight, and so cannot robustly vindicate disenfranchisement proposals. Given these basic decidability and robustness concerns, we conclude that the complaints introduced above fail on the best available grounds that could be offered in their favor. This conclusion is particularly valuable, since it confronts proponents of agebased disenfranchisement policies with both internal and normatively non-committal reasons for discarding their own proposals. The conclusion is also valuable because it avoids examining such proposals on the basis of alternative views about political equality say, equal political dignity or authoritythat straightforwardly reject them, but which might seem question-begging to advocates of equal political influence.
Importantly, our focus on whether there are democratic reasons for disenfranchising older citizens means that we do not examine non-democratic grounds for such proposals for instance, intergenerational justice or social utility. 4 This does not imply that these alternative grounds do not matter; it merely means that our aim here is to construct a narrower analysis of how far democrats can go with these proposals. Though limited, our analysis provides a needed contribution to the literature on the overall justification of agebased disenfranchisement.
The paper is structured as follows. In section 2, we introduce the idea of equal political influence, and situate it in comparison to other ways of understanding political equality. In sections 3 and 4, we reconstruct and examine two arguments about whether older citizens can be disenfranchised under the equal influence view, and assess their policy implications, most notably in terms of age-weighted voting policies. The first argument is a synchronic one: it examines the disproportionate influence that older citizens putatively exert over elections considered in the present time, i.e., at the moment when elections happen. The second argument is diachronic: it examines the disproportionate influence that older citizens putatively exert on elections considered from the point of view of the future. Both arguments, we contend, are hardly applicable and unrobust Section 5 concludes.

Political equality as equal electoral influence
As indicated, our aim is to explore whether a democratic case for the (partial) disenfranchisement of older citizens can be offered. Since political equality lies at the heart of many justificatory accounts of democracy 5 (e.g. Dahl, 1989;Beitz, 1990;Christiano, 2008), plausible attempts to ground such a policy will likely take this value as their starting point.
The idea of political equality can be construed in a variety of ways. For instance, Beitz (1990) distinguishes between best results, popular will, and procedural theories of political equality, Wall (2007) notes that the proper equalisandum can be understood either as political power, political influence, political liberties, or political status, and Wilson (2019) maintains that political equality can be construed either as equal power or as equal authority. Not all accounts will be able to ground even a prima facie reason for age-weighted voting. Consider, as a clear-cut example, Dahl's account which stipulates as a constitutive requirement that "each citizen must be ensured an equal opportunity to express a choice that will be counted as equal in weight to the choice expressed by any other citizen" (Dahl, 1989: 109). Other views, such as those relying on political status or liberties, will also likely undercut any democratic case for age-weighted voting before even getting off the ground. If one of them ultimately turns out to be the uniquely appropriate interpretation of the political equality ideal, it would conclusively count against any democratic argument for age-weighted voting. But, until political equality disagreements are settled, it is worth assessing the best possible democratic argument for such a policy, and to try to construct it with the most favorable normative assumptions in mind.
From the list of plausible accounts of political equality on offer, we believe that appealing to equal opportunity of political influence as an equalisandum makes the most sense. More specifically, we examine the extent to which this equalisandum can be applied to an electoral context in an age-sensitive manner, and whether doing so can generate a sound case for the purported disenfranchisement policies.
Drawing on different available normative accounts of equal political influence, we characterize it as follows. First, elaborating on Brighouse (1996), we understand influence over a decision as an agent's ability to affect the probability that the decision is taken in favor of a specific option among those included in the relevant decisional set, absent knowledge of other agents' preferred option(s). 6 Second, equal influence should not be construed as actual equal influence, but as equal opportunity to influence electoral outcomes. Also drawing on Brighouse (1996), we posit that the point of the equality of influence ideal is not that, for every election, each electorally relevant agent should de facto influence the electoral outcome no matter the costs incurred by that agent. Agents should be able to choose whether they want to influence any given electoral outcome.
Third, equality of opportunity to influence electoral outcomes should be understood as effective, as distinct from merely formal opportunity. This means that the relevant agent should have appropriate and, by comparison, fairly comparable material, social and political means to participate in electionsfor instance, an easy access to the polling station, enough time to vote, non-discriminatory registration procedures, free access to political information, and so on. Absent such means, electors can be said to lack a real opportunity to influence elections.
Fourth, equality of influence is a relative ideal, i.e., an ideal realized among agents in relation to each other, not by looking at the absolute amount of influence that any one agent holds in isolation from others.
Fifth, equal electoral influence should be a justified democratic ideal. This means that equal electoral influence does not justify itself: equal influence is not something we have reason to value intrinsically. In pushing for more equal electoral influence, we should be able to point to the democratic value or principle that equal electoral influence is meant to realize or approximate. Depending on one's conception of democracy, the relevant value or principle can be equal respect (Brighouse, 1996), nonsubordination (Kolodny, 2014a(Kolodny, , 2014b, agency (Baker, 1998) or another democratically compelling value.
A recurrent argument underlying disenfranchisement demands is that older citizens influence elections considerably more than other age-groups, which is considered democratically objectionable. To be sound, this argument cannot be directly cashed out in terms of formal individual inequalities in electoral influence. Formally, each old citizen has the same amount of influence as each younger elector: one vote. For influencebased arguments to work, it seems that they need to be deployed at the group, not the individual level. Moreover, as already indicated, they need to track effective opportunity of influence over elections, not merely formal opportunities.
Whether groups and not individuals are the adequate units for allocating voting rights is a matter that elicits disagreement. Many argue that the right to vote is a right derived from some feature persons have qua individualssay, one's sense of dignity or interest in participating in collective decisions (Douglas, 2013). Others point out that the right to vote might be better specified as a right that protects certain group interests, at least if we understand those interests in a metaphysically light sense, as aggregate interests that individuals have qua group memberssay, the interest to coalesce with like-minded people or the interest to pursue a certain life-style meaningfully realizable only at the group level (Gerken, 2001;Cox, 2007;Beckman, 2017). In fact, arguments that construe voting primarily as a mechanism for the protection of group interests are widespread in the literature on electoral policies. For example, several of the most influential defenses of compulsory voting rely on the claim that raising turnout would effectively advance the interests of lower income and less educated groups in society (Lijphart, 1997), that compulsory voting would solve intra-group coordination dilemmas (Hill, 2015), and that it would mitigate the free-riding behaviour exhibited by non-voters on the interests of their social group (Umbers, 2020).
We are not committed to either one of these two accounts of the right to vote. Rather, we endorse a position whereby both individual and group-level considerations are necessary, but not sufficient, for a full justification of the right to vote. Moreover, as will become clear below, the complaints about older citizens' electoral influence have a natural interpretation at the individual level as well. To wit, the complaints can be cast in terms of a disproportionate amount of electoral influence that an individual has in virtue of belonging to a particular age-group, as compared to individuals belonging to other, discretely distinct age-groups. If this redescription holds, the complaints do not depend on whether the individual or the collective account of voting rights is ultimately the correct one.
Having clarified what equal influence means and the sense in which it can apply to the electoral context in an age-sensitive manner, we will now consider two ways in which older citizens are presumed to hold too much electoral influence. We consider two temporal sequences within which older citizens might be seen as holding unequal influence: synchronicallyi.e., considering the old age group and other age groups at the same moment in timeand diachronically, i.e., considering the old age group at a given moment in time by comparison with other age groups at other momentsin particular, by comparison with other age groups in the future.

Age-weighted votes under the synchronic account
Here, we focus on what the equal electoral influence view might entail for the disenfranchisement of older citizens when we look at different age-groups synchronically. Currently, people who are 65 + stand for between ⅙ and ¼ of the electorate in advanced democracies. 7 In the US, that figure is currently at 23%, and, like in many other contemporary democracies, it is generally projected to increase in the not-so-distant future.
Following Astra Taylor's complaint cited in the introduction, this raises a worry about the disproportionate influence that older citizens have compared to other age groups. To be plausible, the complaint needs to be properly specified: the complaint is not that older citizens have some influence over electoral outcomes, but that their influence is relatively disproportionate when compared to younger age groups. Thus specified, the complaint precludes any full disenfranchisement scheme; at most, it allows for partial disenfranchisement.
Furthermore, the complaint is not about demographics only, but about the dynamics underlying their voting behavior, given the demographics: it argues that, given their number and social position, older citizens exert a problematically higher influence over elections because of their higher turnout, especially as compared to youth turnout. This seems to be true in many contemporary democratic elections. For instance, in the 2018 US midterm elections, 66% of the electors who were 65 + voted, while only 35% of electors aged 18-29 did. 8 Similar turnout patterns exist in other democratic systems. 9 One might reply that turnout is not given but made, and that younger electors have the opportunity to vote in higher numbers, and thus eliminate the turnout gap. More generally, given a roughly balanced demographic structurei.e., one where there is no age group that forms an electoral majority or pluralityunequal influence can better be addressed by other age groups participating in elections more than they currently do. This resonates with the equal opportunity of influence ideal, where equal influence flows from people's voluntary choices. 10 However, this reply doesn't directly address the synchronic complaint, which is that older citizens have an unjustified electoral turnout advantage over younger ones. Properly reconstructed, the complaint is (i) that, given current demographic dynamics, older citizens have more electoral influence because they can participate in larger numbers and (ii) that they participate in larger numbers because they have an age-group advantage consisting in lower opportunity costs in participating. 11 The costs claim has been advanced by Posner (1995: 150), who notes that "voting is cheaper" for older citizens, because their opportunity costs for participation -especially when it comes to the time involved in turning out to vote -are structurally lower. The age-based distribution of opportunity costs matters because it implies that the effective opportunity for influencing elections is not reasonably equal for older citizens as compared to younger ones: the former have a structural turnout advantage that the latter lack. If it is furthermore true that the costs of younger citizens cannot be reduced in democratically legitimate ways, some measure for counterbalancing the latter's disproportionate influence seems required. This could be achieved through an age-weighted voting scheme that would reduce older voters' electoral influence in proportion to their entrenched turnout advantage. Older citizens would thus not be individually deprived of their right to vote, but only partially disenfranchised. Thus reconstructed, the argument for the synchronic complaint runs as follows: P1: equal opportunity to influence elections requires a reasonably equal distribution of structural opportunity costs for electoral participation (SOCEP) P2: old age significantly lowers SOCEP (conversely, young age significantly increases SOCEP), and thus has inegalitarian effects on the distribution of SOCEP P3: given P1 and P2, the inegalitarian effects of old age on the distribution of SOCEP should be counterbalanced P4: the inegalitarian effects of old age on the distribution of SOCEP should be counterbalanced in a way that is compatible with equal opportunity to influence elections P5: age-weighted voting can counterbalance the inegalitarian effects of age on the distribution of SOCEP P6: age-weighted voting does not generate other inegalitarian effects for electoral participation C: age-weighted voting advanced equal opportunity to influence elections In this argument, P1 posits a normative claim, P2 adds an empirical statement, P3 advances a demand informed by P1 and P2, P4 introduces a constraint on how the demand formulated in P3 should be achieved, and P5 and P6 propose an electoral policy that putatively satisfies P3 and P4. In what follows, we examine each premise in turn, thus gaining clarity on the synchronic complaint.
We take P1 as prima facie justified for most supporters of the equal opportunity of electoral influence. Its main contention is that citizens' opportunity to influence elections is not a workable ideal if citizens' costs for electoral participation are unequally hampered or boosted by structural factors, i.e., factors that are not under the citizens' control, but exist as natural obstacles or emerge as social barriers. Such factors might, for example, be the comparatively reduced physical mobility of a particular group of people or the surrounding social culture defining the kind of actions some groups are expected to engage in. Limiting SOCEP to factors that are naturally contingent or socially emergent excludes costs that directly result from people's voluntary choices (e.g. a businessman's opportunity costs for business when voting) or opportunity costs that are imposed through electoral (or other) state policies (e.g. costs tied to the timing of the elections or through registration procedures).
Construing SOCEP as a special category of costs that are neither individually chosen nor state-imposed makes sense on pragmatic grounds. We often assert that the state should reduce some people's participatory costs in electionsfor instance, the costs incurred by citizens born with physical impairments or by citizens who are culturally led to believe that voting is not for thembecause they are not individually chosen and even if they are not imposed through the state's policies alone. SOCEP thus seem to refer to a conceptually distinct category of opportunity costs for electoral participation. Furthermore, insofar as costs falling under SOCEP are examined on the basis of the equality of influence ideal, they are problematic because they disadvantage individuals belonging to particular groups and give others an entrenched participatory advantage over them.
The statement introduced by P2 is (i) that ageing lowers SOCEP and (ii) that SOCEP thus become unequally distributed across age lines, with significantly lower costs for older and higher ones for younger citizens. Based on evidence from 21 European countries, Goerres (2009) singles out three factors that arguably lower older citizens' opportunity costs for participating in elections, namely free time (retirees or people at the end of their careers have more of it), duration of residence (older people are more likely to have lived in the same place for longer) and habituation (older people are statistically more likely to find voting easier simply because they are used to it). Goerres (2009: 66) notes that the "social and cultural construction of our life course sets the scene for a higher likelihood among older people to vote" and argues that, insofar as they supervene on the social fact of ageing, they "stand outside the political process" (17). This means that these factors cannot directly be eliminated or modified through state policies. 12 Conversely, age skews the participatory playing field against younger citizens, in particular against those under 30. 13 If these factors cannot be directly countered through state policy and if they have inegalitarian effects on electoral participation that individuals cannot undo, supporters of the equality of influence ideal might need to counterbalance the effects of agedependent SOCEP. One way to do this would be to design policies that neutralize the effects of the higher SOCEP that fall on younger citizens in virtue of their age. But even if they proved effective, many such interventions might violate our commitment to equal opportunity of influence (as distinct from equal actual influence). Such would be the case with convenience voting schemes, e.g., voting by mail or e-voting, which might neutralize the disadvantage in free time that younger people have, but damage equal opportunity of influence due to the impossibility of ensuring the same ballot secrecy as that provided by the polling booth (in turn, making the exertion of undue pressure on voters easier). Similarly, one-off compulsory voting schemes that could habituate young voters to vote throughout their lifetime (Saunders, 2010) or civic education programs that might achieve the same end do not reduce the unequal costs of influencing elections, but render the choice not to influence electoral outcomes more costly for young voters. This compounds the said structural costs, and thus runs contrary to its professed purpose. Finally, it would be either unfeasible or democratically illegitimate to increase younger citizens' turnout by closely regulating their leisure time or their duration of residence. 14 Thus, many policies meant to neutralize age-induced SOCEP might either fail to meet P3's demand or pass P4's constraint.
Some may argue that the type of structural factors which advantage older people in relation to voting are also encountered if we look at other demographic groups. Take free time. Though empirical evidence is not clear-cut, a number of studies point out that the distribution of free time is still marked by gender inequality (e.g. Mattingly and Bianchi, 2003;Sayer, 2005), with women having less free time and doing more unpaid household work, in spite of the fact that the gap is narrowing. Also, there is some evidence that differences in leisure are also affected by income and education, with richer and more educated individuals having less of it (Aguiar and Hurst, 2007). Since opportunity costs for electoral participation can vary with gender, education, income, and potentially other variables, shouldn't we then recommend mechanisms like the age-weighted voting to reduce the disproportionate influence exercised by male, less educated and lower income citizens?
We can attempt to respond to these claims on a case-by-case basis. Regarding the former, insofar as men have structurally more free time than womensay, because of unjustifiable gendered work-life balance patternsa gender-weighted voting system that reduces men's structurally disproportionate electoral advantage could be justified on the equal influence ideal if it were also true that men are a disproportionately bigger group than women. This conditional statement seems consistent when advanced on equal influence grounds. But the statement is false, and thus blocks the objection. Turning to rich citizens, one might reply that the free time of the rich is not as deeply structuralor, at least, not structural in the same wayas the free time of poor citizens. Additionally, they might contend that the free time of poor citizens is substantively dissimilar from the one of older ones, at least insofar as a considerably bigger share among the former spend some of their "free time" on non-leisurely activities, such as looking for work and making ends meet. Conditional on older citizens actually having free time that is not non-voluntarily spent on labor-intensive activities, one can argue that the inconsistency objection either confuses between two kinds of free time or mischaracterizes the extent to which the poor have more free time than the rich.
We acknowledge that these responses are controversial and those who are unconvinced by them can insist that the advocate of age-weighted voting must extend the same reasoning to other features such as gender or income. This, in turn, would raise a significant problem, not for the synchronic argument itself, but for the practical feasibility of the electoral policy it recommends, since (1) the features requiring weighted voting would become numerous and difficult to meaningfully assess and (2) many of these features can vary with individual choices or unforeseen natural or social circumstances, unlike age which is impervious to such unpredictability. Thus, this feasibility concern represents a serious challenge for any policy based on the synchronic argument.
P5 and P6 hold that age-weighted voting would, unlike the alternatives listed above, satisfy P3 and P4, and thus be at least permissible under the equal electoral influence view. 15 The idea of such a system is not novel, but its justification is. For example, Philippe van Parijs (1998) thinks that introducing an age-based plural voting scheme could alleviate some of our concerns regarding issues of intergenerational justice. While not committing himself to one particular way of operationalizing such a system, he advances two possible alternatives. The first one, which is relevant for this article, would be to give "one extra vote to the under-60s or […] a weight of 2 to the vote of an 18-year-old and having that weight reduced by 1% every year" (van Parijs, 1998: 305). The problem with this way of allocating weights for the argument discussed here, however, is that it either implausibly implies that there is a deep division in SOCEP between senior citizens on the one hand and all other adults on the other one, or that the differences are gradual (which is more plausible), but necessarily increasing in a linear fashion with time (which is less plausible).
In practical terms therefore, it would be difficult to estimate the precise weights by which older citizens should be disenfranchised as a group, even when we know that they hold some SOCEP based on age alone. This is because we lack reliable replications of the empirical findings that point to older citizens having such structurally lower costs, but also because the theoretical models used to detect the advantages that come with lower costs might not be sensitive to age-based disadvantages. To this, advocates of the weighted-voting scheme might reply that we can resort to democratic proceduresfor instance, having the weights decided by deliberative mini-publics composed of ordinary citizens and expertsto circumvent the epistemic difficulties, at least to some extent.
But this reply seems ad-hoc, and does little to assuage worries about disenfranchising older citizens more than their putative entrenched electoral advantage allows. Consequently, the proposed mechanism faces a first serious epistemic hurdle.
Second, it might be that, in some political systems, old age works as a liability rather than an asset when it comes to electoral participatory costs. For instance, there are democratic polities where older citizens are seriously disadvantaged because of age-specific factors, such as reduced mobility or widespread ageist attitudes about whether they should vote at all and, as a result, participate less. 16 When this is the case, defenders of the equal influence ideal might be surprised to find out that what is required is a partial surfranchisement scheme for senior citizens, whereby age-weighted voting would increase older voters' influence in proportion to their age-induced higher SOCEP by granting their vote more weight. To this, advocates of the initial proposal might reply that it comes with scope conditions, and will therefore be applied only where unequally distributed SOCEP that come with old age are an issue. But this would be normatively arbitrary, and fail to satisfy the equal influence ideal as applied to age groups. 17 Taken together, these objections suggest that, even if we take age-weighted voting to be justified, it would be difficult to specify the voting weights, apply it across a relevant range of electoral contexts, and prevent its potentially perverse side-effects.

Age-weighted votes under the diachronic account
One might not endorse the synchronic view examined in the previous section and still worry that older citizens have too much influence diachronically. This captures Geoffrey Downs' complaint about the "65-ers" not having to live as long with the consequences of the Brexit referendum. This is not about structurally unequal electoral participatory costs, but about older citizens having too much influence on elections whose future outcomes will, given their lower life expectancy, either (i) not affect their interests or (ii) affect them significantly less, as compared to those of younger citizens.
To make this complaint democratically palatable, three amendments are required. First, (i) needs to be rejected as false: no matter the election, most older citizens will be affected by its outcome(s), at least to some extent (not all older electors die on election day). Rejecting (i) means that the complaint cannot demand disenfranchising older citizens en bloc.
Second, the complaint cannot get off the ground qua democratic if it targets the ideology that informs how older citizens vote or the substantive consequences of their electoral choices (e.g. negative economic effects). Quibbling about ideological content would deny citizens' basic electoral freedom of choice. Pointing to the consequences of older people's votes cannot be conclusively evaluated before or right after the elections and, even if that were possible, adopting it as a principle for designing electoral policies would de facto lead to renouncing democracy in favor of epistocracy or other non-democratic regimes.
Third, the relation between political equality and time should be properly addressed. In a seminal paper, McKerlie (1989) distinguishes the "complete lives" approach to egalitarianism from alternatives, such as the "corresponding segments view" or the "simultaneous segments view". 18 One might argue that the implications of a complete lives approach will pull in a different direction than the one suggested in the previous paragraph: because life expectancy is continuously on the rise, younger people are generally expected to have more than an equal share of electoral influence throughout their lives compared to older ones, so perhaps their votes should count less.
A corresponding segments approach could have similar implications. For example, if people in the cohort that currently reached seniority spent an important part of their lives in a non-democratic system, disenfranchising the younger generation would be necessary for achieving political equality. Defending any one temporal account of political equality goes beyond the scope of our article, but we note that the simultaneous-segments view favored by McKerlie (1989;) seems more consistent with political egalitarianism as well. McKerlie's view requires that people who occupy different temporal segments in our case, younger and older peoplebe, as much as possible, distributively equal. Like the simultaneous segments view, the diachronic account examined here objects to inequalities between people who occupy different life-stages; additionally, it focuses on a specific equalisandumnamely, the ratio between people's political influence on and the degree to which their interests are affected by elections. The diachronic account requires that this ratio remain equal, which is not true when people have equal influence on elections that affect their interest significantly less. 19 By contrast, both the complete lives and corresponding segments views tolerate nondemocratic political institutions (see also Mraz, 2020: 265-267), as long as people equally alternate between unequal positions. Consequently, if democracy requires that people be in equal positions of some kind at least at some point in time, neither of these two views is distinctly democratic.
Properly amended, the complaint is that it is unjustified for older citizens to have an equal say on elections whose outcomes will have a significantly smaller impact on their relevant interests 20 , be it for the good or for the bad, irrespective of their preferences or convictions, and in relation to younger citizens. Thus reconstructed, the diachronic complaint offers an instantiation of the more general principle of all-affected interests (AAP) that many political philosophers and political scientists have endorsed for drawing the limits of democratic rights in general and of voting rights in particular. Cast in standard form, the diachronic complaint runs as follows: P1: justified equal electoral influence requires that citizens' influence on elections be proportional to their interest-affectedness (i.e. the degree to which their relevant interests are likely to be affected by the electoral outcomes) P2: given their lower life expectancy, some of the older citizens' relevant interests are affected proportionally less by some elections than younger citizens' interests P3: given P1 and P2, older citizens should have proportionally less electoral influence in some elections P4: age-weighted voting ensures that older citizens have proportionally less electoral influence in some elections C: justified equal electoral influence requires age-weighted voting in some elections In the argument above, P1 captures a normative claim, P2 introduces an empirical proposition, P3 states an implication of accepting both P1 and P2, and P4 introduces a policy claim about how P3 can be satisfied. In what follows, we examine each premise in turn, thus gaining clarity on the circumstances under which the diachronic complaint might warrant disenfranchising the old. As before, our aim is not to take a conclusive stance on the normative content of the argument, but to merely analyze and present the prima facie reasons that may count in its favor.
Two objections to P1 can be raised right off the bat, one empirical and one normative. The empirical one is that P1 relies on a link between electoral outcomes and public policy which does not really pan out in representative democracies, since voters do not typically choose policy alternatives, but political competitors, who will subsequently take public decisions directly if they garner enough support. While the claim that in some contexts policy is indeed relatively invariant to the preferences of the majority has been defended (Gilens, 2012), there is a robust literature which argues that policy is generally responsive to turnout demographics (see Malkopoulou and Hill, 2020 for an overview). Consequently, interest representation can be at least partially and indirectly linked to electoral outcomes, which are in turn shaped to some extent by electoral policies. 21 The normative objection is that AAP is not an intuitively plausible democratic principle. But, given that many people (both philosophers and ordinary citizens) do endorse AAP, this would be question-begging. Furthermore, the objection might be at least partly misdirected: P1 does not make a constitutive claim about the boundaries of the demos; rather, it raises a claim about how AAP can be used to structure the decisional power of those who already are part of the demos. To the extent that the objection focuses on the boundary problem, it does not fully apply here.
More specifically, P1 holds that the reason for equal electoral influence is not intrinsic (as posited in the previous section, equal electoral influence is not self-justifying). Rather, following this specification of AAP, justified equal electoral influence is about ensuring that the citizens whose relevant interests are affected by elections can, through their voting rights, influence how those interests are affected. 22 For most elections, the relevant interests belonging to citizens with voting rights are on average equally affected, such that their electoral influence ought to be equal as well, at least following AAP. For example, citizens who can vote for one of the twenty-one regional water boards in the Netherlands all have equal interests in clean water and water safety and, for each regional board, these interests will, for practical purposes, be equally affected. P1 thus introduces a context-sensitive democratic ideal of equality: (i) everyone's relevant interests count equally (C1's interest in clean water is equal to C2's interest in clean water, and so on) and (ii) equal degrees of interest-affectedness count equally. The proposal that equal electoral influence requires citizens' influence to sometimes be proportional to their interest-affectedness is thus not necessarily a departure from equality. Rather, it is as an implication of taking interest-affectedness as a standard for assessing pertinent equality claims. 23 AAP supporters, however, generally disagree about whether proportionality is compatible with (and, more strongly, required by) democratic equality. Some, like Goodin and Tanasoca (2014) argue that, insofar as it's cashed out in voting rights, electoral influence or power should always be strictly equal, and thus voting rights should always be strictly equal as well. This is because the franchise, qua ideal democratic egalitarian institution, ought to give people "equal power over the world", where "power over the world" is a rough shorthand for how we influence the course of events as individual members of existing collectives. According to this view, allowing voting power to vary with the number of interests people have would be undemocratic because it runs counter the "equal power over the world" desideratum (some people might have more interests than others) and because it takes interests instead of persons as unit of normative concern for allocating votes. Call this the Fixed Equal Quantum (FEQ) view.
Others, like Angell and Huseby (2020: 4) argue that, adequately applied, AAP requires that "the weight of a person's vote on a decision should be determined by and only by the degree to which that decision affects her interests, and independently of her voting weights on other decisions". 24 Angell and Huseby (2020) call this the Independent Positive Proportionality (IPP) criterion, and ground it in a more basic principle of autonomy. The contention here is that giving people more weight over the decisions that affect them more enables them to effectively co-author their collective life and honors equality construed as equal interest-affectedness.
If correct, IPP grounds P1. But, irrespective of whether IPP is correct, this brief analysis of the disagreement between AAP adherents shows that there are prima facie reasons to support P1. Furthermore, Goodin and Tanasoca's (2014) worry that proportionality is sensitive to variations in the number of interests across persons does not apply to P1 directly. This is because P1 narrows down the set of interests to relevant ones, and can thus avoid concerns about people's electoral influence contingently varying with any interests people happen to have. Proponents of P1 can claim that the set of relevant interests is the same for everyone (i.e. no one is allowed to raise voting claims on the basis of interests that fall outside that set) and still argue that those interests are differentially affected by some elections. Put differently, P1 makes a claim about varying quantities in interest-affectedness, not about the varying quantities of interests.
No matter where one stands on this general disagreement, there might be room for locally agreeing on P2 and P3. FEQ-supporters worry that, by allowing differences in voting weights, some people might exert more power over the world than others. If one argues from AAP, this matters because more power over the world translates into one having more (and thus unequal) opportunities to affect other people's interests. Intuitively, this violates democratic equality. However, intuitions here might be sensitive to the temporal dimension of the world at issue. The world posited by FEQ is temporally unspecified: we don't know how the effects of people's electoral influence on relevant interests are distributed over time. But time might matter. Consider: Restaurant: Every four weeks, Linda has dinner out with her niece and nephew. This time, they decided to go to a foodsharing restaurant that serves small dishes. The waiter tells them that the restaurant policy is for each customer to have four dishes. Linda is a nurse at a nearby hospital. This evening she's on call, which means that she might have to leave at any moment. Knowing this, Linda decides that she'll choose only two dishes and, to keep in line with restaurant policy, let her niece and nephew choose the other two dishes for her. "After all," she tells them, "I might have to leave not long after they bring the food." In Restaurant, time matters for how the decision to order food is structuredi.e., it matters whether Linda is there to eat what she ordered earlier. The contention here is that some elections are analogous to Restaurant: given life expectancy rates, we know that, on average, older citizens will be less affected by the future outcomes of some elections (P2). This gives them more electoral influence than their interest-affectedness, as distributed through time, warrants. Consequently, their influence on electoral outcomes should be reduced in proportion to their reduced affectedness (P3). Since FEQ rejects weighted votes on the assumption that we all inhabit the same temporally undefined world, and since this is not true in a temporally defined one, there is no clear reason why they would resist P2. Furthermore, insofar as the interests posited in P1 are limited to relevant interests and since P3 is implied by P1 and P2, there is no clear reason why FEQ would reject P3.
But even if we secured local agreement on P2 and P3, P2 seems hard to specify. It is difficult to determine the exact elections where older citizens' interests would tend to be less affected in virtue of their life expectancy. The most plausible candidates here seem to be referendums whereby democratic polities enter (or cancel) international agreements and treatises, join (or leave) supranational organizations or introduce constitutional changes with expected long-term effects that will affect older citizens considerably less. But note that the effects of such referendums might unfold such that older citizens are affected to the same extent and, in some cases, more than younger ones. In-between elections where older citizens' interests are minimally affected (say, a referendum on whether all children should be taught Latin in school) and elections where they are considerably affected (say, a referendum to reduce pensions), we lack a procedure to determine degrees of interest-affectedness. Consequently, even if it is plausible, P2 might turn out to be hardly applicable.
Supporters of the diachronic complaint might reply that P2 could be specified by having the demos voluntarily agree on a subset of elections (referenda or other) where the range of available options is defined so that the relevant interests of older citizens will be known to be affected considerably less. Given the history of referenda and, for most democracies, the open-ended nature of referendial agendas, this seems unlikely. Moreover, the reply looks like an ad-hoc fix to the real epistemic difficulty we are supposed to solve.
Another challenge to the diachronic argument mirrors the one which we initially outlined in the previous section, targeting the inconsistency of taking age and not other demographic variables as criteria for weighted voting. According to a WHO report (2020), the global average life expectancy for men is 69.8 years, while for women it is 74.2 years, leaving a 4.4 years gender gap. Even more significant gaps in life expectancy can be uncovered when looking at income (Chetty et al., 2016) or education, where a study by Meara et al. (2008) reports a widening gap between highly educated and less educated individuals in the US, going from less than 3 years in the early 1980s to 7 years in 2000. If voting rights are to reflect older citizens' life expectancy, should they not also more specifically reflect the reduced life expectancy of men, the less educated and lower income citizens? Again, this would imply that we should extend the principle of weighing votes not only through an age filter, but also taking stock of gender, income, and possibly other features as well.
One might reply that the objection unduly papers over an important normative difference between the average life expectancy at the general society level and life expectancy at the social group level, especially when it comes to disadvantaged groups. The difference is that the latter clearly incorporates a feature that is unjustified from the point of view of equality, with some social groups living less than others (in part) because of objectionable social, economic and political arrangements. Unlike group-specific life expectancies, the general average life expectancy is, strictly speaking, the same for everyone. Consequently, using the general average life expectancy as a criterion for deciding voting weights will not further reduce the electoral influence of people whose social group characteristics render them diachronically less influent than they could have been were it not for the life expectancy inequalities induced by group-specific disadvantages. In short, we have additional equality-sensitive reasons not to use social groupspecific life expectancies that incorporate disadvantages which reduce the life expectancy of some groups as compared to others.
But this reply invites another objection, which is that people with life expectancies higher than averagesay, women, the well-educated and the richwould be unduly disenfranchised under the proposed weighted voting scheme. To this, one might respond that, at least when it comes to women, the life expectancy gap is increasingly narrowing, which means the inequality thus created would not be persistently substantial. Alternatively, one might argue that opportunities for electoral influence should always be evaluated against the background of opportunities for political influence more generally and that, given the reduced opportunities that women have for general political influence as compared to men, we should make an exception to disenfranchisement when it comes to women. But this seems ad-hoc as well, and so consistency dictates that the weighted-voting system account for gender, income, and potentially other variables as well, which raises the strong feasibility concerns we noted in the previous section.
More problematically still, instituting voting weights to reflect the equality between citizens' opportunity to influence elections and the degree to which they are diachronically affected by the outcomes of those elections might mean that, for some other elections than those posited in P2, older citizens should have more voting weights than younger ones. This is because the electoral process is generally reversible, i.e., it allows for prior electoral decisions to be undone over time. But the opportunity to influence electoral outcomes is also temporally bound and by comparison more constrained for older citizens. For elections where citizens' interests are equally affected, older citizens' lower life expectancy might recommend that we grant them more electoral weights to compensate for the higher electoral influence that life expectancy gives to younger citizens. It is uncertain which, if any, elections are strictly like this. Be that as it may, supporters of P2 who endorse older citizens' partial disenfranchisement in some elections might be surprised to discover that they might have to endorse their surfranchisement (i.e. bigger voting weights) for other elections. 25 Suppose that we managed to identify a subset of elections that affect older citizens' interests proportionally less. How should we decide which specific weights are the right ones and how to distribute them across lifecycles? Those who argue for ageweighted voting on grounds other than democracy agree that the weights should reflect life expectancy differentials among different age-groups, but they remain largely noncommittal about the magnitude of those weights. Van Parijs (1998: 305), suggests that one possibility 26 would be "to keep things simple and moderate, one additional vote could be given for each quarter of a century of remaining life expectancy". The reason for preferring this scheme over the alternativessay, Möckli's (1993) proposal to give 18-year-olds 2 votes that decrease by 1% each yearis largely pragmatic.
The equal electoral influence view is, we think, better placed to normatively guide how age-based voting weight sizes should be determined. Remember that the equal electoral influence view worries about influence differentials between age-groups, not between individuals of different ages. As mentioned, this is because an individual's electoral influence is both too small to raise any plausible influence inequality concerns and equal when compared to any other individual's influence.
More specifically, in deciding voting weights and their distribution across age-groups, we should simultaneously try to satisfy our pro tanto reasons for reflecting proportionality in interest-affectedness and our reasons for ensuring equal electoral influence among age-groups. Doing so recommends that both the weights and temporal cut-off points for allocating them be kept relatively small. Because we want voting weights to reflect interest-affectedness on the basis of life-expectancy, we should avoid introducing dramatic differentials among different age-groups. Thus, the proposal for losing 1 vote every 25 or 10 years seems problematic, especially if the maximum voting weight is 3 or 6, as in van Parijs' proposal. However, because we want to ensure some equalitysensitive balance in the influence between different age-groups, we also want to avoid weights and weighting rates so small that they keep influence inequalities among age-groups roughly intact.
Möckli's proposal for 2 votes at 18 and a 1% yearly disenfranchisement rate seems to fit both the proportional interest-affectedness and the age-group influence concerns. It is both smooth enough to avoid dramatic shifts between those who are close to old age and the newly old and substantial enough to ensure that the electoral influence of 65 + -year-olds is, qua age-group, meaningfully smaller than the influence of those aged 18-to-32. 27 Using a strategy that simultaneously tries to satisfy group influence and interest-affectedness when designing an appropriate age-weighted voting scheme has at least two desirable implications. First, determining voting weights with an eye to overall age-group influence means that we have no pressing reason for fully disenfranchising any older citizen, even if this is what proportional interest-affectedness would strictly recommend. This is because the very old are both a very small minority that does not, as such, raise any plausible unequal influence concern and because they are de facto less likely to participate in elections. Because we only care about overall age-group influence, we can therefore introduce a limit to how much anyone can be disenfranchised. We can set that limit at 1 and introduce it when people enter later stages of old age, which is when their electoral turnout generally plateaus. Second, favoring a small disenfranchisement rate allows us to avoid compounding other existing inequalities among demographic or socio-economic groups. For instance, by not reducing voting weights substantially every 25 (or even every 10) years, we avoid disenfranchising those who have considerably lower life expectancy to the same extent as those who have higher life expectancy (the voting weight of a 65-year-old will thus be 10% bigger than that of a 75-year-old). This seems generally desirable from the point of view of equality. 28

Conclusion
In this article, we examined whether disenfranchising older people can be justified on equal political influence grounds. The focus on equal influence as an account of political equality was motivated by our attempt to construct the most fitting defense of current old age-based disenfranchisement proposals. Even under this account, the democratic case for older citizens' disenfranchisement is weak. First, even if the arguments are sound, they cannot vindicate any blanket age-based disenfranchisement, but only schemes whereby older citizens are granted somewhat less weight in elections. Second, if the premises are to be assessed in a consistent manner, age weighted-voting turns out to be hardly applicable and practically unrobust since: (1) the age-relative features which ground partial disenfranchisement cannot be so neatly tracked as to specify a clear assignment of electoral weights to age groups, (2) some age-relative features may actually turn out to require giving more rather than less weight to older citizens, and (3) if we care about consistency, weighted voting might have to be extended to other groups as well, to track variables such as gender or income, which is arguably both normatively undesirable and practically unfeasible.