In The Good Society 5, no. 2 (Spring 1995): 37-39.

Approval Voting on Bills and Propositions

Steven J. Brams


Steven J. Brams is professor of politics at New York University and author of Theory of Moves (Cambridge University Press, 1994) and, with Alan D. Taylor, Fair Division: From Cake-Cutting to Dispute Resolution (Cambridge University Press, 1996).


Bills in Congress

The convening of the 104th Congress in January 1995 raises once again the question of whether anything can be done to save Congress, which has suffered from pretty dismal ratings in recent years, from itself. I believe a straightforward but major reform of its voting procedures, especially in the Senate, would promote a more bipartisan consensus, attenuating the bickering and rancor that pervades Congress today.

The idea is simple. Instead of voting on bills one at a time, Congress would consider several bills on a particular subject, like health care, simultaneously, including the status quo option to do nothing. Rather than being limited to voting for just one bill, however, a member of Congress would be able to indicate all the bills he or she considers acceptable.

This method of voting is known as `approval voting' (Brams and Fishburn, 1983; Brams, 1993). It does not assume that a particular quota, such as a simple majority of 51 votes in the Senate or 218 votes in the House, is needed to enact legislation. Rather, the bill that garners the most approval would win and become law--or the law would stay the same if the status quo were the most approved alternative.

An immediate objection to such an idea is that legislation could pass with only minimal support--say, 30 votes in the Senate, if all the other bills got still fewer votes. To prevent the passage of such fringe legislation, I recommend that all bills on a particular subject, in order to be voted on in the approval-voting contest, would have to gain either the support of more than 1/3 of the members of a relevant congressional committee or more than 1/3 of all House or Senate members as sponsors.

Experience with approval voting in the election of candidates in multicandidate races suggests that the winning alternative would probably garner more than a simple majority. In fact, several alternatives might do so, in which case a bill with, say, 60% approval would beat one with 55% approval.

Amendments may or may not be permitted on the floor of each chamber. (In the House, they are not allowed if a so-called closed rule is in effect.) But if amendments are permitted, the amended bills would simply be new bills to be considered, in addition to the unamended bill, when approval voting is used to vote on the entire set of bills.

Thereby `killer amendments' could not be used to scuttle bills, which might otherwise have won had they not been amended. I would also recommend that filibusters in the Senate, which now require 3/5 of the members to shut off, not be permitted.

The legislators who filibuster should not be dismayed. In lieu of trying to prevent consideration of a bill, they can propose their own alternative. A healthy contest among competitive alternatives would thereby be fostered.

To summarize, I propose that a bill could reach the floor of the House or Senate through more than 1/3 support in a relevant committee or by the sponsorship of more than 1/3 of the entire membership. If amendments are permitted, unamended bills would still remain on the table, also to be voted upon in the approval vote.

Although the idea of less-than-a-majority's proposing, and possibly enacting, legislation may seem strange, an analogous system for the consideration of cases is used in the U.S. Supreme Court, wherein the support of only four or the nine justices is required to grant a case review.

True, a simple majority of at least five justices is needed to render a decision. But deciding a case is a very different matter from putting together complex legislation in Congress, in which several reasonable packages may vie for support.

This was indeed the case with health-care legislation in the last Congress, but never were the several proposals considered together in one vote. Even if they had been, it is conceivable that the status quo might still have been the most approved alternative.

But among, perhaps, ten or twenty packages that might have been proposed--all `reasonable' in the sense that each would already have had substantial support--I believe at least one might have defeated the status quo. It is a shame that congressional procedures possibly blocked such a consensus choice.

Propositions in Referendums

To illustrate the advantages of using approval voting on referendums, I turn to a concrete case. On November 7, 1990, California voters were confronted with a dizzying array of choices on the election ballot: 21 state, county and municipal races, several local initiatives and referenda, and--most important from the standpoint of approval voting--28 statewide propositions. These propositions concerned such issues as alcohol and drugs, child care, education, the environment, health care, law enforcement, transportation, and limitations on terms of office.

Using the set of ballot images produced by 1,672,793 nonabstaining voters (i.e., who voted yes or no on at least one of the 28 propositions) in Los Angeles county in the 1990 election, I focus on the following three related propositions on the environment (Brams, Kilgour, and Zwicker, 1995):

P130. Forest Acquisition Initiative, which would ban clear-cutting in all forests, authorize a $742 million bond issue for the purchase of redwood forests, and place certain restrictions on the harvesting of timber, the burning of debris from logging, and the export of logs.

P148. Water Resources Bond Act, which would authorize $340 million for various water projects, including water storage and drought assistance, water treatment, and flood control.

P149. Park, Recreation, and Wildlife Enhancement Act, which would authorize $437 million in bonds to acquire, develop, and restore parks, beaches, and other recreational areas and pay for forest fire stations, museums, and zoos.

Not only do these propositions seem to be related, but they were all closely contested in Los Angeles county: P130 passed 49% to 44%; P148 failed 44% to 42%; and P149 passed 46% to 42%. The remaining votes in each case were abstentions.

Because all three propositions were pro-environment and involved the expenditure of substantial funds, there is good reason to believe that many voters saw them as related. Additional evidence for this view is the fact that the propositions polarized the voters. Cross-tabulations of the numbers of voters choosing yes (Y), no (N), and abstention (A) for each pair of propositions show a remarkable grouping of voters. For example, on P148 and P149, 34% of the voters favored both propositions (YY) and 33% opposed both (NN). Of the remainder, the largest group (10% of the total) abstained on both (AA). Altogether, more than 3/4 of the voters agreed in their views by voting Y, N, or A on both propositions.

The situation for the other pairs was similar. On P130 and P148, 29% voted YY and 29% voted NN. On P130 and P149, 33% voted YY and 29% voted NN. Not only did many voters take the same positions on all pairs, but large numbers took the same positions on all three propositions. In fact, of the eight Y-N combinations--we exclude those that include one or more As--the five most popular combinations selected by voters on P130, P148, and P149, respectively, are as follows (their numbers of their supporters are shown in parentheses):

YYY (430,807); NNN (422,916); YNN (129,729); NYY (128,153); YNY (99,176).

The winner was not YYY, however, but YNY: Y won on P130, N on P148, and Y on P149, as I indicated earlier. Yet, as a combination, YNY was supported by only 5.9% of the voters. By contrast, YYY was supported by 25.7%, and NNN by 25.3%, of all voters.

The fact that YNY came in a distant fifth, with less than 1/4 of the support that the YYY and the NNN combinations received, may seem surprising. Even more surprising, if not paradoxical, is that it is theoretically possible for the combination that comes in last of the eight possible combinations, and therefore has the fewest supporters, to be the winner, based on the plurality contest on each proposition. This discrepancy between the proposition-by-proposition plurality winner and the combination winner was first noted in Brams, Kilgour, and Zwicker (1994), who showed that it generalizes the so-called Condorcet paradox that leads to cyclical majorities. I shall give a real-life example of this paradox later.

To be sure, it might be argued that the unpopular YNY is a reasonable compromise between the 25.7% who voted YYY and the 25.3% who voted NNN. But YNN and NYY, because each received more direct support (7.7% and 7.8%, respectively) than YNY (5.9%), could also make this claim.

The choice between relatively unpopular compromises (e.g., YNY, as well as YNN and NYY) and the more popular `pure' positions (e.g., YYY and NNN) is hard to resolve simply on theoretical grounds alone. I believe approval voting, when used directly on the combinations, would offer voters a desirable resolution by enabling them to make more refined choices.

To illustrate, YYY supporters might also vote for YYN, YNY, or NYY to indicate that Ys on two of the three propositions, or some subset of these, are acceptable. Similarly, NNN supporters might also vote for NNY, NYN, or YNN to indicate that Ns on two of the three propositions, or some subset of these, are acceptable.

On the other hand, those voters whose first choice is one of the six mixed Y-N sets could indicate that YYY or NNN is also acceptable--and perhaps one or more of the other mixed combinations as well. Finally, there might be some voters who favor both YYY and NNN over all the mixed combinations, believing that halfway measures are worse than all (YYY) or nothing (NNN).

If approval voting had been used to vote on the eight Y-N combinations of P130, P148, and P149, it is difficult to say--from the (restricted) actual choices of voters--what combination would have been the most popular. Although approval voting often favors compromise alternatives, such as one of the mixed combinations, the fact that the two pure combinations, YYY and NNN, received more than three times as many votes as any of the mixed combinations, under the extant system, suggests that one of these all-or-nothing combinations might have won.

If so, however, it almost certainly would have done so with substantially more than the roughly 25% support that YYY and NNN each received under plurality voting. As one measure of comparison, Bill Clinton would have increased his 43% plurality vote in the 1992 presidential election to about 55% approval (Brams and Merrill, 1994); with eight alternatives on the ballot rather than the three major ones on the 1992 presidential ballot, it is not implausible that the winning combination might have received about 50% or more approval.

I emphasize, however, that it is anything but clear whether the winning combination would have been one of the pure or one of the mixed combinations. Regardless, arranging the ballot in terms of combinations of a few related propositions, and giving voters the option of voting for more than one, would enable them better to express their preferences.

Such a restructuring of permissible individual choices would give greater coherence to a process that now, unfortunately, often produces a grab bag of winning propositions that few if any voters support as a package. In fact, not a single one of the 1.7 million Los Angeles county voters voted for the winning combination across all 28 propositions (P124-P151)--namely, for NNNYNNYNYNNNNNNYNYNYNYYNNYNY. This referendum, by the way, provides an empirical example of the paradox mentioned earlier: a winning combination may receive the fewest votes.

Grouping the 28 propositions on the 1990 California ballot into, say, ten packages of two or three related propositions--each with 4-8 combinatorial choices--would, perhaps, double or triple the number of choices of voters to about 60-90. This is a large number, suggesting that more stringent criteria for putting propositions on the ballot might be introduced. More difficult to come up with might be principles for grouping propositions into a few packages that present voters with reasonable choices, but this would not seem to be an insurmountable obstacle.

These difficulties notwithstanding, it seems evident that the results of voting on the three environmental propositions led to an outcome whose legitimacy is questionable. Not only would another outcome probably have been selected if there had been approval voting on combinations of these propositions, but, arguably, it would have been more socially desirable.


Approval voting, though now widely used in universities and professional societies (Brams and Fishburn, 1992), has not, as far as I know, been seriously considered for voting on bills in Congress--or in other councils or legislatures--or for voting on related propositions in referendums. In both settings, it seems an eminently sensible if radical reform. However, what propositions are `related,' and therefore should be packaged as combinations in referendums, may not be an easy practical question to resolve.


Brams, Steven J. (1993). `Approval Voting and the Good Society.' PEGS Newsletter 3, no. 1 (Winter): 10-14.

Brams, Steven J., and Peter C. Fishburn (1983). Approval Voting. Cambridge, MA: BirkhŠuser Boston.

Brams, Steven J., and Peter C. Fishburn (1992). `Approval Voting in Scientific and Engineering Societies.' Group Decision and Negotiation 1 (April): 41-55.

Brams, Steven J., D. Marc Kilgour, and William S. Zwicker (1994). `A New Paradox of Vote Aggregation.' Preprint, Department of Politics, New York University.

Brams, Steven J., D. Marc Kilgour, and William S. Zwicker (1995). `How Should Voting on Related Propositions Be Conducted?' Preprint, Department of Politics, New York University.

Brams, Steven J., and Samuel Merrill, III (1994). `Would Ross Perot Have Won the 1992 Presidential Election under Approval Voting?' PS: Political Science and Politics 27, no. 1 (March): 39-44.