The Role of Argument in Negotiation

The purpose of this paper is to show the pervasive, though often implicit, role of arguments in negotiation dialogue. This holds even for negotiations that start from a difference of interest such as mere bargaining through offers and counteroffers. But it certainly holds for negotiations that try to settle a difference of opinion on policy issues. It will be demonstrated how a series of offers and counteroffers in a negotiation dialogue contains a reconstructible series of implicit persuasion dialogues. The paper is a sequel to van Laar and Krabbe (2017), in which we showed that for some differences of opinion it may be reasonable to shift from persuasion dialogue, aimed at a resolution of the difference on the merits, to negotiation dialogue, aimed at compromise, whereas in the present paper we show that such a shift need not amount to the abandonment of argumentation. Our main aim in this paper as well as in the previous one is to contribute to the theory of argumentation within the context of negotiation and compromise formation.


Introduction 1
When trying to develop a reasonable compromise by means of negotiation dialogue, one may expect that argumentation plays an important role. As we shall see, argumentation has a role to play in what appears to be pure interest-based bargaining. Even more evident is its role in negotiations about policy issues between parties with conflicting interests and with different views on what would objectively be the best policy to adopt. In such negotiations parties will be seeking a compromise that settles not only their differences of interest but also their differences of opinion. Which is not to say that these differences would be resolved as in the case of a successful persuasion dialogue.
Within the field of argumentation studies, various authors have called attention to the role of argument in contexts of negotiation (Walton 1998, Chapter 4; van Eemeren 2010, pp. 149-150), and some have studied how compromise and negotiation dialogue relate to argumentation and persuasion dialogue (Amgoud and Prade 2006; van Veenen and Prakken 2006;Mohammed 2007;Ihnen 2016). Yet, there is no detailed theory available about how making an offer connects to argument, how making a counteroffer connects to criticism, and how the exchange of argument and criticism may assist the disputants to step-wise develop a mutually agreeable compromise that settles their difference of opinion.
Consider the following example of compromise formation: In 2012, two Dutch political parties, the Labor Party (PvdA) and the Liberal Party (VVD) agreed to form a coalition government, despite their various differences. To just focus on one cluster of issues, they differed with respect to renewable energy and climate change. The Labor Party favored a policy of increasing the level of renewable energy to 18% in 2020 and of abolishing taxes on self-generated electricity from solar panels, whereas the Liberal Party supported policies of increasing the level of renewable energy to just 14% in 2020 and of maintaining taxes on self-generated electricity from solar panels. The discussants, apparently, had not been able to convince their interlocutors of the objective worth of their own action proposals; yet they were willing to search instead for a compromise that, though each might conceive it as only a second choice, all would be willing to accept as fair and preferable to a lasting conflict (which would delay the formation of a government and might even lead to a completely different government by other political parties). At the end of their negotiation process, they did arrive at a compromise, which presumably indicates that each became convinced of the expediency of the compromise arrived at. It is highly plausible that argumentation has played a role in the coalition talks, even though no minutes of them are available. In this paper we develop a view on the role of argumentation in the development of a compromise that splits a difference of opinion.
As we shall explain in Sect. 2, we follow Mohammed (2007) and van Eemeren (2010) in dealing with negotiation dialogue as a communicative activity type, or as a genre of such types, in which argumentation is of key importance. At the same time, our approach diverges from their approaches, as we shall explain.
In a persuasion dialogue about policy issues, the parties try to convince one another of the acceptability of their preferred policy options in a cooperative attempt to resolve a difference of opinion on the objective merits of both sides. A negotiation dialogue, on the other hand, is aimed, not at resolving a difference but at settling it by developing a deal, which both parties conceive of as expedient, based upon a trade of material or non-material items. 2 A failure of parties to find or create a resolution of their difference by means of a persuasion dialogue may prompt them to shift to negotiation dialogue, provided that they seriously reckon with the feasibility of an expedient compromise that will settle (though not resolve) their difference of opinion. In our first paper on splitting differences of opinion (van Laar and Krabbe 2017, Section 2.2 and 2.3; see also van Laar and Krabbe 2016, Section 2.2) we discussed various reasons that may motivate the parties to shift from persuasion to negotiation dialogue, in a shared attempt to split a difference of opinion (rather than a difference of interest). Next to the practical reason that thus it may be possible to realize at least some of their aims, more principled reasons may motivate them to take this route. Among these one may find the wish to be democratic, the wish to foster a sense of community, and the wish to act in an epistemically virtuous way.
By shifting to negotiation dialogue a party could possibly commit the Fallacy of Bargaining, i.e. the fault of shifting illicitly from persuasion to negotiation dialogue when one of the participants does not agree to the shift or is not even aware of the shift's taking place (Walton and Krabbe 1995, p. 110). However, the Fallacy of Bargaining can be avoided by obtaining the interlocutor's (explicit or implicit) consent, for example by means of the various motivating reasons for turning to negotiation dialogue.
In the same papers (van Laar and Krabbe 2017, Sect. 3;2016, Sect. 3), we compared the outcomes of a successful persuasion dialogue to that of a successful negotiation dialogue. We started from Weinstock's notion of a compromise: ''a compromise is a position that, with respect to the issue at hand, is from the point of view of parties locked in debate or negotiation inferior to the positions that both (or all) bring to a decision making process (…), but which both have reason to accept instead of the position they favor. They may favor X, when only the issue at hand is in view, but favor Y when all things are duly considered'' (Weinstock 2013, p. 539).
Yet, somewhat differently from Weinstock, we considered a compromise to be some kind of agreement, namely an agreement on an arrangement that both have reason to accept, notwithstanding its being considered by all parties as inferior to the positions they brought to the decision making process. We emphasized a number of key features of compromise. First, a compromise is not a resolution. After all, a compromise requires genuine sacrifices from both sides, and each party subscribes to the outcome only because a general acceptance of what one considers being the best policy is beyond reach. Second, compromise is not imposed, but the outcome of a sufficiently non-coercive process-even though we acknowledge that some kinds of pressuring and rewarding are legitimate in negotiation dialogue. Third, a compromise is based on a kind of trade. At some point, the participants must go along with a way of dealing with their difference of opinion as a problem of distributing items, such as promises to act or to refrain from certain actions, thereby ''commodifying'' their opinions. Fourth, compromise brings a commitment to the proposition that, ''when all things are duly considered,'' including the (real or alleged) circumstance of there being an irresolvable and adverse disagreement about what policy to pursue, the compromise policy merits acceptance. Fifth, compromise may yield resolutions of actual or potential second-order disagreements, such as the disagreement about what policy to settle for in the special circumstance where parties are involved in an adverse and irresolvable first-order dispute about what policy to adopt.
In the present paper, we continue our study of argumentation in relation to negotiation and compromise formation, doing so by examining the role of argumentation within a negotiation dialogue with a special focus on negotiation dialogue that has its origin in a difference of opinion. To make progress on this issue, we first, in Sect. 2, deal with the role of argumentation within a bargaining dialogue aimed at settling a mere difference of interests. The result we put to use when analyzing, in Sect. 3, the role of argumentation in negotiation dialogues in which the parties are trying to develop a mutually acceptable compromise that settles an unresolvable difference of opinion. Section 4 summarizes our findings.

Argumentation in Negotiation
In the introduction we stressed the difference between persuasion dialogue and negotiation dialogue but in this section we shall deal with the dialectic of exchanging offers and compromise proposals and show that much of negotiation dialogue consists of or can be reconstructed as persuasive arguing. We examine how an interest-based bargaining dialogue may allow of an argumentative reading, and proceed, in the next section, by applying this way of reading a bargaining dialogue to the kind of negotiation dialogue with which parties may, in a reasonable way, try and settle differences of opinion about action proposals. Van Eemeren (2010) characterizes negotiation as a conventionalized genre of communicative activity types in which the interlocutors start from a conflict of interests, and typically aim at a mutually accepted compromise by exchanging offers and counteroffers, which often incorporate argumentation (pp. 149-151). 3 We agree that negotiation dialogue can best be seen as a genre of activity types in which participants exchange offers and counteroffers, and we likewise emphasize the role of argumentation in negotiation, which we want to specify here. Mohammed (2007) already offers a more elaborate analysis of how argumentation gets incorporated within the argumentative activity type of a negotiation, and we share her view that ''a negotiation encounter can usually be broken into many disputes, each of which is marked by a new advanced position, and each can be subject of pragma-dialectical analysis'' (977a). We shall list some notable differences between her and our analysis at the end of this section. At this point, we merely want to point out that we conceive of each (counter)offer as conveying an argument that can be modeled as an persuasion dialogue embedded within the negotiation dialogue. Thus in this paper we deal with persuasion dialogue (like negotiation dialogue) as a conventionalized genre for which norms are proposed by the pragma-dialectical model of critical discussion. 4 The following exchange can be seen as a typical example of bargaining, i.e. an interest-based negotiation dialogue that is mainly made up from offer and counteroffer. In order to serve their individual interests, a piano salesman and a customer need to cooperate to reach a deal as well as to compete to sell the piano for a high or to buy it for a low price. The dialogue participants assume that there are outcomes available that they both value above no deal, so that that if we would conceive of their interaction as a game, it would not be a constant sum or zero sum game, notwithstanding the fact that in the exchange of offer and counteroffer, potential gains for the one are sacrifices for the other, and vice versa.
We may bring out the quid pro quo (in the sense of ''my concession in return for your concession'') character of the various contributions more clearly by conceiving of the utterances as elliptical sentences, the expanded versions of which read: The piano dialogue, version 2 Although no reasoning is being made explicit in the expanded version, this bargaining plausibly depends upon an exchange of reasons. As we have discussed at an earlier occasion (Krabbe and van Laar 2007, pp. 29-30), the interpersonal reasoning that is characteristically expressed in a negotiation dialogue fulfills a directive function: The arguer reasons either (1) in order to make the addressee understand that his or her proposals are unrealistic and thereby to make the addressee mitigate his or her demands or (2) to make the addressee understand that the arguer's proposal would provide a satisfactory outcome of the negotiation and thereby to make the addressee accept the proposal or at least propose a counteroffer that approaches the arguer's proposal. We consider reasoning that is used in some situation of conflict (either a personal antagonism, a difference of interest, or a difference of opinion) with the purpose of overcoming doubt by means of reasons (either doubt regarding the proper intellectual or social relationship amongst the parties, or regarding the way of distributing scarce resources, or regarding the acceptability of opinions) as reasoning with an argumentative function (2007, p. 31). Thus, reasoning with a directive function is one kind of reasoning with an argumentative function, and we shall elaborate on that function by way of a further analysis of our dialogue example. 5 It's not hard to reconstruct the argumentative message of the directive reasoning in our example by conceiving of it as an exchange of what we label as ''expediency arguments from consequences'' or shortly as ''expediency arguments.'' An expediency argument is an instantiation of the following argumentation scheme (cf. Walton et al. 2008, pp. 332-333, on the more general argumentation scheme ''argument from consequences''): The argumentation scheme ''Expediency Argumentation from Consequences'' Premise 1: Party X's acceptance of offer Y has consequences Z. Premise 2: Consequences Z serve party X's interests. Conclusion: It is expedient for party X to accept offer Y.
If the parties negotiate in a way that goes beyond mere pressuring and that contains serious attempts to convince one another of the acceptability or unacceptability of particular compromise options, we can understand the quid pro quo moves more or less implicit in the negotiation dialogue as appealing to, and thereby conveying, expediency arguments by which the speaker attempts to convince the interlocutor of the acceptability of a proposed compromise (offer), given the interlocutor's own value-assignments. Take for example the salesman's first turn: Turn 1, Salesman: The Salesman makes an offer: ''I am prepared to give you this piano if you are willing to give me 7000 euro.'' By making the offer the salesman takes on the role of proponent of the thesis that it is expedient for the customer to accept his proposal and presents Argument 1 in support of his thesis: ''(Premise 1.1) If you would accept my offer of selling you the piano for 7000 euro, you would obtain this piano for 7000, and (Premise 1.2) you really value this piano at 7000 at least. Therefore, (Conclusion 1.3) it is expedient for you to accept my offer.'' Thus by making this offer, the salesman creates and expresses a persuasive argument that appeals to the customer's interests, hoping that the argument's premises are acceptable or at least hoping that the customer is willing to put forward a counterproposal that will do justice to the salesman's interests conveyed by proposing 7000 as an acceptable price.
Turn 2, the customer's counterproposal, contains three components. First, there is an implicit message of turning down the salesman's first proposal. This message can be reconstructed as a critical response towards Argument 1, and towards Premise 1.2 in particular. Second, there is the explicit counterproposal. Third, in her counterproposal the customer can be seen to, implicitly, advance a thesis of her own, accompanied by a new expediency argument from consequences: Turn 2, Customer: The Customer takes on the role of opponent vis-à-vis Argument 1, and advances the following criticism: ''I do not value this piano at 7000 at least.'' Also, she tables a new offer: ''I am prepared to pay you 6000 euro if you give me the piano.'' By doing so, she adopts the role of proponent of the thesis that it is expedient for the Salesman to adopt her counteroffer, and she presents Argument 2 in its support: ''If you would accept my offer of buying the piano for 6000 euro, you would earn 6000, and you really value this piano at 6000 at most. Therefore, it is expedient for you to accept my proposal.'' In her critical response to the salesman's offer the customer is legitimately appealing to what is and is not in her own interest, while in her attempt to persuade her interlocutor of her own proposal she is appealing to the addressee's interests. The present critical response is to be expected in either of two situations. One possibility is that the customer considers 7000 to be less desirable than no deal. In other words, the maximum price she is willing to pay is lower than 7000, for example because the shop next door offers a comparable piano for 6900. 6 The other possibility is that she thinks the deal to be more desirable than no deal but expects to be able to get an even better deal from the salesman. Of course, also in the second kind of situation, the customer may state or suggest for tactical reasons that she find herself in the first kind of situation, thereby putting pressure on the salesman to mitigate his demands.
More in general, it can be expected that appeals to one's own interests must be understood as the explanation of why a proposal is rejected (or accepted), and also as giving hints to the interlocutor about the kind of offers (theses) that might successfully be argued for in one of the upcoming negotiation rounds. Instead, appeals to the addressee's interests must be seen as ex concessis argumentation, that is, as attempts at convincing an opponent to accept a particular offer, based upon premises that the opponent is willing to accept.
Turn 3, Salesman: Criticism of Argument 2, in the role of opponent: ''I do not value this piano at 6000 at most.'' New offer: ''I am prepared to give you the piano if you are giving me 6500.'' He adds the warning that in any future negotiation round where the customer offers less than 6500, he will not accept the proposal. In a situation where there is reason to expect that the parties try to convince one another on reasonable grounds, a bargaining exchange of offer and counteroffer can be analyzed as including an interlocked series of local argumentative moves. The first move of the exchange contains just an expediency argument; all other moves but the last one comprise a critical response towards the previous offer, a new offer, and a new expediency argument; and the last move consists either of an acceding response to the other's latest offer and argument or of some other (less positive) move ending the negotiation dialogue. In this systematic search for a solution that is acceptable to both, each critical response provides information about the interests of the speaker and directs the interlocutor towards an offer that consists of a successful expediency argument based upon concessions that the speaker is willing to make. Bargaining can thus be reconstructed as containing a series of argumentative exchanges about what the participants want, about how much they want it, and about the expediency of particular choices in the light of information about the existing preferences, which gradually becomes available. 8 Each pair consisting of an expediency argument in one turn and a critical or acceding response in the next turn can be seen as a small persuasion dialogue revolving around one thesis and embedded within the exchange of offer and counteroffer that constitutes the main course of the negotiation dialogue. 9 According to this argumentative reading of negotiation, a successful compromise is in a special way connected to the resolution of a difference of opinion, for the reason that a progressive series of persuasion dialogues, each about a distinct thesis, finally concludes with a persuasion dialogue that results in a full resolution (in our example: the persuasion dialogue in which argument 4 is presented). Figure 1 shows how we conceive of the exchange of argument and criticism that accompanies an exchange of offer and counteroffer in a negotiation dialogue starting from a difference of interest. The top left solid box corresponds to turn 1 by the salesman; the top right solid box corresponds to turn 2 (by the customer); the bottom left solid box corresponds to turn 3 (by the salesman); and so forth. Each dashed box shows to what persuasion dialogue each part of a turn belongs. Each persuasion dialogue consists of one argument for a conclusion, which one party tries to make acceptable for the other party, and a reaction by this other party.
This argumentative reconstruction of bargaining is plausible in so far as it can be presumed that the participants are attempting to convince one another on reasonable grounds. In some situations, this is certainly not the case: Think, for example, of negotiation contexts in which a participant is by manipulative tricks lured into believing that some offer would be expedient, or in which he or she is by blackmail or bribe pressured to accept an offer, instead of accepting the offer by light of an autonomous estimation of its expediency. The more manipulation plays a role the less the result may count as a compromise (Margalit 2010). But then, in many other situations, the bargaining is based on genuine and continually updated estimates of what might be acceptable for the other so that it will be amenable to an argumentative reconstruction.
We saw that the hard-core exchange of offer and counteroffer in a bargaining dialogue allows of an argumentative reading, even if the argumentative messages are not made fully explicit. Holzinger has shown how the exchange of offer and counteroffer is often supplemented by other types of argument, different from what we have identified as expediency arguments from consequences (Holzinger 2004). By such supplementary arguments, the level of argumentativeness can certainly be increased. The result will be a more explicitly argumentative kind of negotiation. For example, the salesman might in the third turn of the piano conversation choose to add a reason: Turn 3', Salesman: ''6500, and not one euro less. For this piano has quite a nice sound.'' Such an additional reason can be reconstructed as functioning simultaneously as a part of a critical response to the interlocutor's preceding offer and as a new part of the arguer's defense of his own offer.
Turn 3', Salesman: Criticism of Argument 2: ''I do value this piano at more than 6000. To explain myself: It has quite a nice sound.'' Salesman, in his capacity of proponent, advancing Argument 3': ''It is expedient for you to accept my proposal and buy the piano for 6500 euro, because that would give you this piano for 6500, and you really value this piano at 6500 at least. You do value this piano at 6500 at least, because, as I told you, it has quite a nice sound.'' When such additional arguments are not advanced, the bargaining can be seen as being aimed at finding a compromise that is based on fixed preferences. By adding such arguments, the participants try to modify the preferences from which the negotiation started.
To end this section, let us compare the way we reconstruct negotiation with the approach of Mohammed (2007). Mohammed reconstructs negotiation as a series of distinct critical discussions. According to her analysis, an offer can be understood as the adoption of a position, rooted in an interest, to the effect that the other side should perform some action (in her example of bargaining: buying or selling a brass dish for a specific price) which position is supported by an argument: that the other should accept the offer because it would satisfy ''the maximum of the parties' conflicting interests'' (p. 977a). A rejection of an offer, then, is typically justified with a reason that rebuts that this specific offer would satisfy the maximum of their mutual interests (e.g., in Mohammed's example, the reason that the brass dish is dented). Mohammed writes about her example: This negotiation exchange is typical of negotiation occurring at an interpersonal level, in haggling that takes place between customers and shopkeepers. In this negotiation dialogue, a customer and an antique shopkeeper are having a bargain over the price of a brass dish. In this bargain, each of the parties presents an initial position, and they both revise their initial positions in light of the objections they get from the opponent. That is done again and again; whenever a party objects to the advanced position, the opponent revises his own position and introduces a new one. Argumentation is often provided either to support the position advanced, or the rejection of the opponent's position. (977b) We list four differences between Mohammed's account and ours: 1. According to our account, the proponent of an offer only needs to argue in support of the offer's being expedient for the interlocutor, rather than arguing in support of the offer's being expedient, let alone maximally expedient, for both. We think an exchange of such expediency arguments is more in line with the distribution of labor that is typical for negotiation; all the same, it provides the participants with a method for arriving at an optimal outcome. 2. According to our account, each counteroffer can be reconstructed as containing a denial of a premise in the interlocutor's previous expediency argument, even when no specific argument is advanced against the previous offer. In consequence, each counteroffer both adds to the persuasion dialogue about the expediency of the previous speaker's offer as well as to a newly initiated persuasion dialogue about the current speaker's new offer. We think that even a mere exchange of offers and counteroffers, without any supplementary arguments, allows of a plausible argumentative reconstruction in which the parties respond to one another, be it minimally.
The Role of Argument in Negotiation 559 3. As said before, we reconstruct a negotiation dialogue as an exchange of offer and counteroffer, and conceive of the implicit arguments that play a role, as well as of the additional explicit arguments, as part of embedded persuasion dialogues. We do not want to suggest that the exchange of offer and counteroffer can be reduced to an exchange of argument and counterargument. 4. In the next section, we extend our account of negotiation to the settlement of differences of opinion about practical issues; thus we do not restrict our account to differences of interest, as Mohammed seems to do.
All these differences are a kind of subtle. What we want to stress is that our account and Mohammed's are structurally quite similar.

An Argumentative Reading of Splitting a Difference of Opinion
We now want to apply the argumentative way of understanding bargaining dialogues and, generally, negotiation dialogues starting from a difference of interests to negotiation dialogues starting from a difference of opinion about action proposals. For this we return to the difference of opinion between the Labor Party and the Liberal Party in Sect. 1. Remember that, in the coalition talks of 2012, the Labor Party favored a green policy of increasing the level of renewable energy to 18% in 2020 in combination with abolishing taxes of self-generated electricity from solar panels, whereas the Liberal Party favored an economizing policy of increasing renewable energy to only 14% in combination with maintaining taxes on solar panels. When trying to build a coalition, the negotiators of the two parties may or may not have started their discussion of these issues with a persuasion dialogue. If they did, let us suppose that no resolution could be found and that therefore a proposal to shift to negotiation was accepted. Imagine further that the Labor Party tables the following opening offer: ''If you accept the 18% level for 2020 and forgo your demand to restrict the increase to only 14%, we would be willing to accept to maintain taxes on solar panels and forgo our demand to abolish those taxes.'' The negotiation dialogue into which the two parties now enter is somewhat more complex than the dialogue between the salesman and the customer. In the latter dialogue, it is plausible that the degree to which the one party would profit from any outcome quite closely matches the degree to which the other party pays for it. In the current dialogue, however, it is plausible that solutions can be developed that are, for both parties, more advantageous than other solutions, so that they will be preferred by both parties. Those compromise candidates that do not allow of a revision that is preferred by both parties can be labeled ''efficient'' compromise solutions, 10 and one compromise candidate can be characterized as more or less likely to be efficient than another one. 11 The exchange of expediency arguments can be expected to lead the participants in the direction of an efficient outcome. When a compromise is accepted, both parties will generally assume that there is no other compromise solution available that would be better for both of them, i.e. they will assume that the compromise is efficient. Indeed, no offer will be tabled unless its proponent considers it to be maximally advantageous for himself in the social context at hand, i.e. unless he thinks that any offer that would be more advantageous for himself would not be acceptable for his opponent. Also, no offer will gain the acceptance of the opponent unless the accompanying expediency argument will convince her that, in this context, this offer will yield for her the best achievable outcome, i.e. that a counteroffer yielding a better outcome for her would not be acceptable for the proponent. Each expediency argument will be critically probed, and if a participant supposes an offer to be deficient she will challenge one of the argument's premises. 12 The Liberal Party may respond in various ways to the Labor Party's opening offer. First, the liberals could accept the offer, and close the deal. Second, they could reject the offer and table a counteroffer based upon the same method of distributing items, saying for example: ''If you accept our 14% and forgo your 18%, we would be willing to accept an abolishment of taxes on solar panels and forgo our demand to maintain them.'' Third, they could table a counteroffer based on a different method of distributing items, saying for example: ''Let's settle on a moderate increase of only 16% and only a moderate taxation of solar panels by introducing some kind of fiscal benefit.'' Both counteroffers would provide the Labor party with information that this party can exploit in order to devise a countercounteroffer, if not yet satisfied. In the first counteroffer the liberals disclose their willingness to accept an abolishment of taxes on solar panels as part of a future compromise, and in the second counteroffer they show the softening and moderation of their demands to be a real option. Whereas the details of the actual negotiations are not available, it is known that the outcome has been that the two parties that constituted the coalition government of 2012 opted for this last option of moderation: They decided to subscribe to the compromise of 16% renewable energy in 2020 and some fiscal benefits for producers of renewable energy (Visser 2012).
This kind of exchange shares many features with a bargaining process such as displayed in the dialogue about the price to be paid for the piano. And given the political setting, it is even more plausible to conceive of the exchange as an exchange of expediency arguments and critical responses. In this political setting, which originates from a difference of opinion, it is clear that the items that are traded are promises, namely promises to support particular measures, policies or laws. Note that the bargaining dialogue can also be seen as a trade of promises between parties, namely promises regarding what to exchange to one another if they close a deal. What is, however, distinctive of negotiation in the present setting of a difference of opinion about policy issues is that the parties also attempt to solve the second-order problem of how to cope with the irresolvable disagreement about the first-order policy issues (see van Laar and Krabbe 2017, Sect. 3, for a more detailed treatment of this aspect of splitting differences of opinion).
In the case of the negotiation dialogue between the Labor Party and the Liberal Party, the Labor party's initial offer could be reconstructed as follows: Turn 1, Labor Party: Offer: ''18% renewable energy in 2020 and maintaining taxes on solar panels.'' By tabling this offer, the Labor Party also adopts the role of proponent of the thesis that it is expedient for the Liberal Party to accept its proposal, and supports this thesis by means of Argument 5: ''(Premise 5.1) If you would accept our offer of having 18% renewable energy in 2020 and maintaining taxes on solar panels, you would reach your goal of maintaining these taxes at the expense of having to agree with 18% instead of 14% renewable energy in 2020, and (Premise 5.2) for you it would be expedient to accept this higher percentage of renewable energy in order to secure maintenance of taxes on solar panels. Therefore, (Conclusion 5.3) it is expedient for you to accept our proposal.'' And the possible criticisms implicit in the Liberal Party's counteroffer, whether or not this offer is based on the same method of distributing items as used by the Labor Party, may be reconstructed thus: Turn 2, Liberal Party: Criticism of Argument 5, in the role of opponent: ''For us it is not expedient to accept this higher percentage of renewable energy in order to secure maintenance of taxes on solar panels.'' In the role of opponent, the Liberal party criticizes Premise 5.2, but does so without providing any supplementary argumentation to substantiate her criticism. The Liberal Party could, for instance, have done so in either of the following two ways: (a) 13 ''For us, it's not expedient to accept this higher percentage of renewable energy in order to secure maintenance of taxes on solar panels as we prefer to have no deal rather than this deal'' or (b) ''For us, it is not expedient to accept this arrangement as we expect a better outcome to be available to us''.
Especially the first way would have put some pressure upon the Labor Party to advance an offer that is more attractive to its opponent. But keeping silent about the reasons for one's rejection has about the same effect. A strategic advantage of presenting the criticism targeting Premise 5.2 in this manner, is that it pressures the interlocutor without the critic's committing herself to anything more.
Assuming that the Liberal Party opts for a counteroffer without changing the method of distributing items, the remainder of Turn 2 can be reconstructed as follows: Turn 2, Liberal Party (continued) New offer: ''14% renewable energy in 2020 and abolishment of taxes on solar panels.'' In the role of proponent of the thesis that it is expedient for the Labor Party to accept its counteroffer, the Liberal Party advances Argument 6: ''(Premise 6.1) If you would accept our offer of having 14% renewable energy in 2020 and abolishing taxes on solar panels, you would reach your goal of abolishing these taxes at the expense of having to agree with 14% instead of 18% renewable energy in 2020, and (Premise 6.2) for you it would be expedient to accept a lower percentage of renewable energy in order to secure an abolishment of the taxes on solar panels. Therefore, (Conclusion 6.3) it is expedient for you to accept our proposal.'' Figure 2 shows, analogously to Fig. 1, how we conceive of the first two turns of the dialogue as we image it to have taken place.
If at some point one party in the role of proponent succeeds in giving an argument that gets the approval of the opponent, the parties know they can close the deal. The most recent offer has become the ground for an agreed upon compromise solution.
In van Laar and Krabbe (2017), we showed that for some differences of opinion it may be reasonable to shift from persuasion dialogue, aimed at a resolution of the difference on the merits, to negotiation dialogue, aimed at compromise. In the preceding sections we showed that such a shift does not amount to the abandonment of argumentation, since negotiation itself is permeated with arguments. In the section that follows we shall briefly sketch how, after a compromise has been concluded, argumentation has still an important role to play.

Defending a Negotiated Compromise
When negotiators have reached a compromise, this compromise will usually still need to be approved by others. A compromise concluded by negotiators of political parties in coalition talks (as in the case above the Labor Party and the Liberal Party) must still officially be approved by these parties, say at a party convention, and preferably also by (potential) supporters outside the party. Thus in each of the participating parties the question whether to accept the compromise will be raised and arguments will be needed to defend the compromise. Here we cannot go into these matters in great detail (see however van Laar and Krabbe 2018), but shall just formulate a configuration of two argumentation schemes for what we expect to be the typical structure of a complex argument in support of an agreed upon compromise, as well as a list of typical critical challenges with which to examine the adequacy of instantiations of this argumentation scheme. The configuration of argumentation schemes called the ''Defense of a Negotiated Compromise'' consists of two single argumentation schemes and can be stated as follows: The configuration of argumentation schemes ''Defense of a Negotiated Compromise'' (Standpoint) You should endorse (ratify) this compromise, because (Reason 1) by doing so we achieve X at the expense of Y, and (Reason 2) although we sacrifice Y, this arrangement of achieving X at the expense of Y is preferable to not accepting this compromise.
(Reason 2) Achieving X at the expense of Y is preferable to not accepting this compromise, because (Reason 2.1) an arrangement of achieving X at the expense of Y is preferable to a situation in which the issue is not settled by means of a compromise, (Reason 2.2) as well as to alternative arrangements that happen to have been, still are, or will become feasible outcomes of a (possibly: reopened) negotiation dialogue.
When this pattern of reasoning is put to use to vindicate a compromise, the supporters of party P who are critically testing the argument can advance at least the following challenges: Focusing on Reason 1: Will we actually achieve X? Did the other party really promise that? And if so, is the other party to be trusted to provide us with X? Does Y comprise all the disadvantages of the compromise?
Focusing on Reason 2.1: Is gaining X at the expense of Y really preferable to the consequences of not accepting this compromise? Are we certain enough that the gains will exceed the losses? Wouldn't it be better to stick to the status quo and accept the disagreement? Is this compromise an honorable and legitimate outcome? Did we heed the rights of the stakeholders? Is the compromise legally sustainable? Didn't we sell-out our fundamental principles? Aren't there objections against the other party that ought to prevent us from cooperating with this party?
Focusing on Reason 2.2: Isn't there a better deal that can be closed? With the same or with different parties? For example, a deal in vaguer terms so that it is less binding on us in the future? Or a deal in more specific terms so as to make it more binding on the other party? Did we perform sufficiently well in the negotiation dialogue? Or could we renegotiate a deal with more concessions from their side or with fewer concessions from our side? Is it better to close this deal or must we try to obtain a different one at some future moment?
This list of possible challenges provides us with a first idea of the issues that a compromise gives rise to, when it comes to the argumentative discussion between negotiators that have concluded a compromise (or those that already agree with them) and critical supporters of their party.

Conclusion
Some scholars in political philosophy have emphasized the differences between negotiation and argumentation, for example by understanding bargaining as a nonargumentative exchange of threats and promises (see for such a view, Elster 1995). On the basis of our investigation, however, we tend to be more sympathetic to the recent trend in political philosophy to emphasize the feasibility of a kind of negotiation that aims at a reasonable outcome based on sound reasoning, for example by understanding negotiation as a form of ''political deliberation'' (see for such a view: Mansbridge et al. 2010).
First, we have found that a negotiation dialogue starting from a difference of interest, even if it consists of mere bargaining, can be analyzed as a process that implicitly contains a series of short argumentative discussions so that it can be plausibly understood as being, for an important part, of an argumentative character. Next we showed by way of an example that the same holds for negotiation dialogues starting from a difference of opinion. According to our analysis, negotiation dialogues are accompanied and facilitated by an exchange of expediency arguments from consequences and critical responses to them. This also applies to negotiation The Role of Argument in Negotiation 565 dialogues that originate from a failed attempt to find a substantial resolution of a policy dispute. Thus, argument has a role to play in splitting differences of opinion in a reasonable way, and the shift from a persuasion dialogue about a difference of opinion to a negotiation dialogue about the same difference (van Laar and Krabbe 2017; see also van Laar and Krabbe 2016, Sects. 1, 2 and 3) does not amount to the abandonment of argument. We conclude this exploration into the connections between negotiation and argumentation by emphasizing the need for further investigations of the argumentative aspects of compromise formation, whether within political discourse or in other adversarial settings.