acl acl2010 acl2010-6 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Beata Beigman Klebanov ; Eyal Beigman
Abstract: We present a game-theoretic model of bargaining over a metaphor in the context of political communication, find its equilibrium, and use it to rationalize observed linguistic behavior. We argue that game theory is well suited for modeling discourse as a dynamic resulting from a number of conflicting pressures, and suggest applications of interest to computational linguists.
Reference: text
sentIndex sentText sentNum sentScore
1 edu Abstract We present a game-theoretic model of bargaining over a metaphor in the context of political communication, find its equilibrium, and use it to rationalize observed linguistic behavior. [sent-2, score-0.82]
2 We argue that game theory is well suited for modeling discourse as a dynamic resulting from a number of conflicting pressures, and suggest applications of interest to computational linguists. [sent-3, score-0.206]
3 1 Introduction A 13 Dec 1992 article in The Times starts thus: The European train chugged out of the station last night; for most of the day it looked as if it might be stalled there for some time. [sent-4, score-0.151]
4 It managed to pull away at around 10:30 pm only after the Spanish prime minister, Felipe Gonzalez, forced the passengers in the first class carriages into a last minute whip round to sweeten the trip for the European Community’s poor four: Spain, Portugal, Greece and Ireland. [sent-5, score-0.168]
5 Apart from an entertaining metaphor provides read, the extended an elaborate conceptual cor- respondence between a familiar domain of train journeys and the unfolding process of European Eyal Beigman Washington University in St. [sent-14, score-0.663]
6 Carriages are likened to nation states; passengers to their peoples; treaties to stations; politicians to responsible rail company employees. [sent-17, score-0.199]
7 In a compact form, the metaphor gives expression to both the small and the large scale of the process. [sent-18, score-0.525]
8 So apt was the metaphor that political fights were waged over its details (Musolff, 2000). [sent-22, score-0.649]
9 “There is a fear that the European train will thunder forward, laden with its customary cargo of gravy, towards a destination neither wished for nor understood by electorates. [sent-24, score-0.086]
10 c As2s0o1c0ia Atisosnoc foiart Cionom fopru Ctaotmiopnuatla Lti on gaulis Lti cnsg,u piasgtiecs 698–709, The metaphor proved flexible enough for further elaboration. [sent-31, score-0.525]
11 The fact that European policy is being communicated and negotiated via a metaphor is not surprising; after all, “there is always someone willing to help us think by providing us with a metaphor that accords with HIS views. [sent-46, score-1.077]
12 ”2 From the point of view of the dynamics of political discourse, the puzzle is rather the apparent tendency of politicians to be compelled by the rival’s metaphorical framework. [sent-47, score-0.366]
13 Thatcher tries to turn the train metaphor used by the pro-EU camp around. [sent-48, score-0.588]
14 Yet, assuming metaphors are matters of choice, why should Thatcher feel constrained by her rival’s choice, why doesn’t she ignore it and merely suggest a new metaphor of her own design? [sent-49, score-0.726]
15 In this article, we use the explanatory frame- work of game theory, seeking to rationalize the observed behavior by designing a game that would produce, at equilibrium, the observed dynamics. [sent-52, score-0.395]
16 Specifically, we formalize the notion that the price of “locking” the public into a metaphorical frame ofreference is that a politician is coerced into staying within the metaphor as well, even if he or she is at the receiving end of a rival’s rhetorical move. [sent-53, score-1.032]
17 Since the use of game theory is not common in computational linguistics, we first explain its main attributes, justify our decision to make use of it, and draw connections to research questions that can benefit from its application (section 2). [sent-54, score-0.174]
18 Next, we design the game ofbargaining over a metaphor, and find its equilibrium (section 3), followed by a discussion (section 4). [sent-55, score-0.449]
19 Different moves yield different utilities for a player; it is assumed that each player would pick a strategy that maximizes her utility. [sent-57, score-0.339]
20 The observable is the actual sequence of moves; importantly, these are assumed to be the optimal outcome (an equilibrium) of the relevant game. [sent-58, score-0.091]
21 A popular notion of equilibrium is Nash equilibrium (Nash, 1950). [sent-59, score-0.55]
22 For extensive form games (the type employed in this paper), the notion of subgame perfect equilibirum is typically used, denoting a Nash equilibrium that would remain such if the players start from any stage of the evolving game (Selten (1975; 1965)). [sent-60, score-0.738]
23 The task of a game theorist is to reverseengineer the model for which the observed se2Capitalization in the original, Bolinger (1980, p. [sent-61, score-0.174]
24 The resulting model is thereby able to rationalize the observed behavior as a naturally emerging dynamics between agents maximizing certain utility functions. [sent-64, score-0.301]
25 , 1995; von Neumann and Morgenstern, 1944); in biology the operation of natural selection processes (Axelrod and Hamilton, 1981 ; Maynard Smith and Price, 1973); in social sciences political institutions, collective action, and conflict (Greif, 2006; Schelling, 1997; North, 1990). [sent-66, score-0.178]
26 In recent applications in linguistics, pragmatic phenoma such as implicatures are rendered as an equilibrium outcome of a communication game (J¨ ager and Ebert, 2008; van Rooij, 2008; Ross, 2007; van Rooij and Schulz, 2004; Parikh, 2001 ; Glazer and Rubinstein, 2001 ; Dekker and van Rooy, 2000). [sent-67, score-0.605]
27 For example, computing the equilibrium of a zero-sum game is equivalent to LP optimization (Luce and Raiffa, 1957); an equilibrium of general bimatrix games can be found using a pivoting algorithm (von Stengel, 2007; Lemke and Howson, 1964). [sent-69, score-0.724]
28 While game theoretic models are not much utilized in computational linguistics, they are quite attractive to tackle some of the problems computational linguists are interested in. [sent-71, score-0.174]
29 in terms that reflect agendas of the actors, such as political agendas in legislatures (Quinn et al. [sent-78, score-0.288]
30 , 2001), or social agendas in speed-dates (Jurafsky et al. [sent-80, score-0.136]
31 Game theoretical models are well suited for modeling dynamics that emerge under multiple, possibly conflicting constraints, as we exemplify in this article. [sent-82, score-0.105]
32 3 The model We extend Rubinstein (1982) model of negotiation through offers and counter-offers between two players with a public benefit constraint. [sent-83, score-0.372]
33 The model consists of (1) two players representing the opposing sides, (2) a set of frames X⊂Rn compact and convex, (3) preference relXat⊂ioRns described by continuous utility functions U1, U2:X→R+, (4) a sequence of frames X0⊂X1 . [sent-84, score-0.339]
34 ⊂:2XX→ →thRat can be suggested to the public, ⊂anXd (5) a sequence of public preferences over frames in Xt for t=0, 1, 2, . [sent-87, score-0.264]
35 described by a public utility sf iunn Xction Utp. [sent-90, score-0.374]
36 In odd rounds player 1 appeals to the public with a frame At1∈Xt|Ft, Xt|Ft={A∈Xt : A⊂Ft}, player 2 counters with a frame At2∈Xt|Ft . [sent-93, score-1.056]
37 TAh⊂eF public ycehro 2os ceosu one so wf tthhe a ffrraammees A ba∈seXd on Utp(Ati) with ties broken in 1’s favor. [sent-94, score-0.225]
38 The accepted frame becomes the current frame for the next round Ft+1. [sent-95, score-0.366]
39 In even rounds the parts of players 1 and 2 are reversed. [sent-96, score-0.151]
40 , Ft−1 gives the history of the bargaining process up to t. [sent-100, score-0.157]
41 A strategy σi of player i is a function specifying for any history h={F0, . [sent-101, score-0.246]
42 , Ft−1} the move player ri nmyak heiss oatr yti hm=e{ t, namely the} ftrhaem me Aveti she chooses to address the public. [sent-104, score-0.213]
43 describes a path the bargaining process can take, leading to an outcome ∩t∞=0Ft. [sent-108, score-0.215]
44 pTrhoec players’R utility fdoirn an o auntco omuteco ims given by Ui=limt→∞ RFt Ui (x)dχFt for i=1, 2 where χFt is a probabilityR measure on Ft. [sent-109, score-0.149]
45 If ∩t∞=0Ft={x} the utility is the point utility of x oft ∩herwise= {itx i}s tthhee expected utility on the intersection set. [sent-110, score-0.447]
46 1 Player utility For a given issue under discussion, such as European integration process, we order the possible 700 states of the world along a single dimension that spans the policy variations proposed by the different players (politicians). [sent-112, score-0.331]
47 The utilities of the different players can… i&n;'+" this case be described as continuous single-topoe faakset d functions over an interval. [sent-123, score-0.155]
48 4 Thus X=[0,… …1 b] ta int isd the utility functions Ui (x)=φ( | |x vi | |) forreg vi∈X where φ is a monotonically strictly desclorweears itnhgan function and | | | | is Euclidean distance. [sent-124, score-0.149]
49 2 Public utility We note the difference between two types of utilities: The utility of the players is over outcomes, the utility of the public is over sets of outcomes (frames). [sent-126, score-0.784]
50 The latter does not represent a utility the public has for one outcome or another, but rather a utility it has for an enhanced understanding. [sent-127, score-0.642]
51 Thus, the public’s utility from a frame is a function of the information content of the proposed frame relative to the current frame, i. [sent-128, score-0.515]
52 4Single-peakedness is a common assumption in position modeling in political science (Downs, 1957). [sent-132, score-0.124]
53 frame at time t is Ft then for any Borel set A⊂Ft Utp(A)=Π(Entt(A)) Entt(A)=−µt(A) log µt(A) for a continu- the public where utility fotrh eAn iosr ous probability measure µt on Ft and Π is a continuous, monotone ascending function; for A6⊂Ft, Utp(A)=0. [sent-136, score-0.557]
54 Game dynamics At every point in the game, a certain set of the states-of-affairs is being deemed sufficiently pro- bable by the public to require consideration. [sent-139, score-0.33]
55 Sup- pose that initially any state of affairs within the in- terval [0, 1] is assigned a uniform probability and thus merits public attention. [sent-140, score-0.294]
56 Each in her turn, the players propose to the public to concentrate on a subset of the currently considered states of affairs, arguing that those are the likelier ones to obtain, hence merit further attention. [sent-141, score-0.374]
57 The metaphor used to deliver the proposal describes the newly *proposed subset in a way that makes those statesodfin-ga ffairs that are in it aligned with the metaphor, whereas all other states are left out of the proposed meeed taphorical frame. [sent-142, score-0.562]
58 As the game proceeds, the ep uwbe’ll i gco attention is concentrated on successively esrms aller sets of eventualities, and these are given a more and more detailed metaphoric description, providing the educational gratification of increasingly knowing better and better what is going on. [sent-143, score-0.259]
59 At each step, each player strives to provide maximum public gratification while leading the public to focus on the frame (i. [sent-144, score-0.893]
60 6 Figure 2 sketches the frame negotiation through train metaphor, from some point in time when the general train metaphor got established, through Thatcher’s flashing out the issue of excessive speed and unclear direction, Major’s multi-track corrective, and reply of his opponents on the left. [sent-147, score-0.873]
61 This is different from models of cheap talk such as Aumann (1990), Lewis (1969) where communication is devoid of strategic moves and is used primarily as a coordination device. [sent-149, score-0.242]
62 4 The equilibrium A pair of strategies (σ1 , σ2) is a Nash equilibrium if there is no deviation strategy σ such that (σ, σ2) leads to an outcome with higher utility for player 1 than outcome of (σ1 , σ2) and the same for player 2. [sent-153, score-1.307]
63 A subgame are all the possible moves following a history h={F0, . [sent-154, score-0.257]
64 , Ft}, in our case it is equivaa hleinstto rtoy a game with an ,in iintia olu frra cmasee Ft iasn deq tuhiecorresponding utilities. [sent-157, score-0.174]
65 A pair of strategies is a subgame perfect equilibrium if, for any subgame, their substrategies are a Nash equilibrium. [sent-159, score-0.452]
66 Theorem 1 In the frame bargaining game with single-peaked preferences 1. [sent-160, score-0.481]
67 There exists a canonical subgame perfect equilibrium path F0, F1, F2, . [sent-161, score-0.452]
68 For any subgame perfect equilibrium path F00, F10, F20, . [sent-166, score-0.452]
69 The theorem states that the outcome of the bargaining will always be a frame on the canonical path. [sent-170, score-0.435]
70 The rivals would suggest more specific frames either until convergence or until a situation where any further specification would produce a frame that “misses their point,” so-to-speak, by removing too much of the favorable outcome space for both players. [sent-171, score-0.313]
71 The idea of the proof is to construct a pair of strategies where each side attempts to pull the publicly accepted frame in the direction of its peak utility point. [sent-176, score-0.418]
72 We show, assuming the peak of the first mover is to the left of peak of the second, that any deviation of the first mover would enable the second to shift the public frame more to the right, to an outcome of lower utility to the first mover. [sent-177, score-0.86]
73 Modeling the public preferences as highest relative entropy subset of possible states-of-affairs, we show that strategic choices by the politicians lead to a subgame perfect equilibrium where the less politically extreme player who moves first is at an advantage. [sent-183, score-1.161]
74 In a democracy, such player would typically be the government, as the bulk of voters do not by definition vote for extreme views, and since the government is the agent that brings about changes in the current states of affairs, and is thus the first and most prepared to explain them to the public. [sent-184, score-0.282]
75 Indeed, Entman’s model of frame activation in po- litical discourse is hierarchical, with the govern702 ment (administration) being the topmost frameactivator, and opposition and media elites typically reacting to the administration’s frame (Entman, 2003). [sent-185, score-0.429]
76 In political communication specifically, metaphor has long been known as a framing device. [sent-188, score-0.783]
77 Metaphors are notorious for allowing subliminal framing, where the metaphor seems so natural that the aspects of the phenomenon in question that do not align with the metaphor are seamlessly concealed. [sent-190, score-1.097]
78 For example, WAR AS A COMPETITIVE GAME metaphor emphasizes the glory of winning and the shame of defeat, but hides the death-and-suffering aspect of the war, which makes sports metaphors a strategic choice when wishing to arouse a pro-war sentiment in the audience (Lakoff, 1991). [sent-191, score-0.82]
79 Such subliminal framing can often be effectively contested by merely exposing the frame. [sent-192, score-0.116]
80 Far from being subliminal or covert, the details of the metaphor, its implications, and the evaluation promoted by any given version are an important tool in the public discussion of a complex political issue. [sent-194, score-0.396]
81 The measure of success for a given version of the frame is its ability to sway the public in the evaluative direction envisioned by the author by providing sufficient educational benefit, so-to-speak, that is, convincingly rendering a good portion of a complex reality in accessible terms. [sent-196, score-0.438]
82 Once a frame is found that provides extensive education benefit, such as the EUROPEAN INTEGRATION AS TRAIN JOURNEY above, a politician’s attempt to debunk a metaphor as inappropriate risk public antagonism, as this would be akin to taking the benefit of enhanced understanding away. [sent-197, score-0.961]
83 Thus, rather than contesting the validity of the metaphoric frame, politicians strive to find a way to turn the metaphor around, i. [sent-198, score-0.657]
84 Our results show that being the first to use an effective metaphor that manages to lock the public in its framework is a strategic advantage as the need to communicate with the same public would compel the rival to take up the metaphor of your choice. [sent-201, score-1.7]
85 To our knowledge, this is the first explanation of the use of extended metaphor in po- litical communication on a complex issue in terms of the agendas of the rival parties and the changing disposition of the public being addressed. [sent-202, score-1.075]
86 It is an open question whether similar “locking in” of the public can be attained by non-metaphorical means, and whether the ensuing dynamics would be similar. [sent-203, score-0.357]
87 3 Social dynamics This article contributes to the growing literature on modeling social linguistic behavior, like debates (Somasundaran and Wiebe, 2009), dating (Jurafsky et al. [sent-205, score-0.284]
88 The latter literature in particular sees the social activity as an unfolding process, for example, detecting the onset and resolution of a controversy over the content of a Wikipedia article through tracking article talk7 and deletion-and-reversion patterns. [sent-211, score-0.277]
89 Somewhat similarly to the metaphor debate discussed in this article, Vi´ egas et al. [sent-212, score-0.645]
90 Finding out how the initial contribution constrains and guides subsequent edits of the content of a Wikipedia article and what kind of argumentative strategies are employed in persuading others to retain one’s contribution is an interesting direction for future research. [sent-214, score-0.118]
91 For example, Somasundaran and Wiebe (2009) built a system for recognizing stance in an online — debate (such as pro-iPhone or pro-Blackberry on http://www. [sent-218, score-0.089]
92 5 Empirical challenges We suggested that models of dynamics such as the one presented in this article be built over data where entities of interest are clearly identified. [sent-231, score-0.189]
93 This article is based on chapters 1 and 2 of the book by Musolff (2000) which itself is informed by a corpus-linguistic analysis of metaphor in media discourse in Britain and Germany. [sent-232, score-0.641]
94 The tasks that have been addressed are explication of the reasoning behind the metaphor (Barnden et al. [sent-236, score-0.525]
95 , 2002; Narayanan, 1999; Hobbs, 1992); detection of conventional metaphors between two specific domains (Mason, 2004); classification of words, phrases or sentences as metaphoric or non-metaphoric (Krishnakumaran and Zhu, 2007; Birke and Sarkar, 2006; Gedigian et al. [sent-237, score-0.239]
96 Extended metaphors are expected to be difficult for such approaches, since many of the clauses are completely situated in the source domain and hence no local incongruities exist (see examples on the first page of this article). [sent-241, score-0.201]
97 2 Data collection Supervised approaches to metaphor detection need to rely on annotated data. [sent-243, score-0.525]
98 Another approach is metaphor “harvesting” hypothesizing that metaphors ofinterest would occur in close proximity to lexical items representing the target domain of the metaphor, such as the 4 word window around the lemma Europe used in Reining and L ¨onneker-Rodman (2007). [sent-248, score-0.726]
99 Given the central role played by the public gratification constraint in our model, would conversational situations without the need to persuade the public, such as meetings of small groups of peers or phone conversations between friends, tend less to the use of extended metaphor? [sent-261, score-0.301]
100 Conversely, does the use of extended metaphor in other settings testify to the existence of presumed onlookers who need to be “captured” in a particular version of reality as in pedagogic or poetic context? [sent-262, score-0.555]
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