Stuck in Space:
The Neglected Importance of Issue Salience for Political
Competition
Scott L. Feld
Department of Sociology
Louisiana State University,
Baton Rouge, Louisiana
Bernard Grofman
Department of Political Science
and
Institute for Mathematical Behavioral Science
University of California, Irvine
Prepared for presentation at the European Public Choice Society annual meeting, April
26-28, 2003, Aarhus, Denmark. This research was partially supported by National
Science Foundation grant SBR 97-30578 (to Grofman and Anthony Marley), Program in
Methodology, Measurement and Statistics. We are indebted to Clover Behrend for
library assistance.
ABSTRACT
Virtually all work on electoral competition assumes that candidates compete in
terms of the issue platforms they offer, and that they sequentially search for winning
positions by changing the nature of their platforms. This standard Downsian approach
neglects the fact that candidates are often largely trapped in terms of what policy
platforms they can credibly espouse by their past positions and by the positions voters
attribute to the parties they represent. If candidate locations are largely or entirely fixed,
it might seem inevitable which one will win and which one will lose! However,
candidates can also compete by persuading voters to change the salience of the different
issue dimensions. We argue that competition over issue salience has been wrongly
ignored. We show that, taken two issue dimensions at a time, this competition can be
viewed in two mathematically equivalent ways: as a fight over what will be the new
single axis of cleavage on which voter choices will be arrayed, or as a fight over the
relative weights (w/1-w)of the two existing issue dimensions. Even though candidate
locations are fixed, we show that, unless the voting game has a core and one of the
candidates is located at that core, there will always be one or more axes of cleavage on
which each of the candidates will be victorious. Thus, even though "stuck in space," no
candidate is ever doomed to defeat. Candidates can seek to move the electorate toward a
cleavage axis on which they are winning by persuading the electorate to change the
relative salience voters attaches to each of the two existing issue dimensions. We provide
a geometric framework to understand how issue dimension weightings affect candidate
choice
We show that, even though there is always at least one axis of cleavage on which
each candidate will win, there is also a paradox of non-monotonicity in that a candidate
who seeking to change the relative salience of the two existing issue dimensions so as to
move voter choices to an axis of cleavage on which s/he is winning must risk the near
certainty that the "route" to that winning outcome does not involve a monotonic increase
in votes for that candidate. In particular, we show that, contrary to intuition, weighting a
particular dimension more heavily need not have a uniformly favorable impact on the
election chances of the candidate who is on the more popular side of that issue
dimension. Indeed, ceteris paribus, as we increase the relative weight of an issue
dimension over the range from zero weight (in which case, say, candidate A wins) to
100% weight (in which case candidate B wins), we can get a non-monotonic pattern of
electoral consequences in which first A, then B, then A, then B, etc., is the majority
winner. . Thus, movement in the desired winning direction may actually generate losses
before it generates gains; or a complex pattern of losses, then gains, then losses, then
gains, etc. Nonetheless, if one candidate is extreme and one is moderate with respect to
the set of voter ideal points, we also show that the moderate candidate is relatively well
buffered against attempts by his opponent to change voter perceptions of relative issue
salience, since only dramatic changes in salience weights will lead to that candidate's
defeat. On the other hand, when candidates are roughly equally centrally located wrt
voter ideal points, then issue salience matters a great deal. Even small changes in relative
issue dimensions weights may change the outcome. In sum, while platform locations
matter, so does salience. Both must be taken into account in understanding political
competition.
As the Downsian model has been operationalized by most authors, it implies that
voters have fixed issue locations and that candidates compete for votes by where they
locate in the issue space, with the voter assumed to vote for the party/candidate who is
located closest to the voter’s own most preferred location. Thus, the driving force of
political competition is each candidate's choice of an issue platform.
Skaperdas and Grofman (1995: 57) argue that this portrait of political competition
omits at least four key factors: “(1) the information conveyed by candidates is not only
about putative issue positions but also about candidate attributes such as competence or
trustworthiness; (2) almost invariably, candidates not only characterize themselves and
their own policy positions but also see to (mis)characterize their opponent and their
opponent’s policy positions as well; (3) in a world of multidimensional issue competition,
candidates not only seek to convey the positions they wish to be attributed to themselves
and to their opponent but also often seek to persuade voters that some dimensions (some
issues) are more important than others; and (4) voters do not believe all they are told.”
Also missing from the simple Downsian model are features of choice such as the role of
partisan identification (Campbell, Converse, Miller and Stokes, 1960), retrospective
voting (Fiorina, 1981) and incumbency advantage (King and Gelman, 1991; Feld and
Grofman, 1991). Here, however, our focus will be limited to extending the basic
Downsian model by looking at one important aspect of political persuasion, attempts at
manipulation of the salience of the various issue dimensions.
Downs himself, in perhaps the least cited aspect of his classic work, emphasizes
the importance of political persuasion (1957, 83-84).1 The importance of political
persuasion has also recently been stressed by authors such Zaller (1992) and Lupia and
McCubbins (1998), with a number of recent studies of the effects of negative
campaigning (Ansolabehere and Iyengar, 1995; Skaperdas and Grofman, 1995;
Wattenberg and Brians, 1999; Lau et al., 1999).
1
Downs’ views on political persuasion are discussed in Grofman (1987) and
Weatherford (1993). (See also Grofman and Withers, 1993.)
Political realignment is often modeled in terms of the introduction of new issue
dimensions or the changing salience of the previously existing issue dimensions that
structure electoral conflict (see esp. Schattschneider, 1960; Riker, 1982). More generally,
Riker (1986) has argued that the heresthetic "framing" of issues helps decide who wins.
Also relevant to the model we offer in this paper are the work of authors in the spatial
modeling literature who study the jurisdictional structure in a legislature in a setting
where each committee determines the outcomes on a single issue dimension (see esp.
Feld and Grofman, 1988; Humes, 1993). These authors look at the geometric structure of
the set of generalized medians, i.e., the platforms consisting of median locations on each
issue dimension, as we rotate the underlying axes that define the issue space.
Perhaps most directly relevant to the work we present here is the model in
Hammond and Humes (1993). They consider two-candidate competition in twodimensional space in a game where each candidate is associated with a single dimension
and "controls" the angle of rotation of one of the two axes of cleavages that define this
two-dimensional space. In this game voters are posited to choose whichever candidate is
closest to them on one of the dimensions. For fixed voter and candidate locations, they
show examples in which outcomes will depend upon which (not necessarily orthogonal)
axes of cleavage are chosen by each of the candidates. In closely related work, authors
such as Jones (1994) and Lawson (2000) have looked at the impact of changing issue
salience on voter choice.
Our general concern in this paper will be with incorporating issue salience into
models of political campaigning in two-candidate competition over two (or more
dimensions). We assume that either candidate positions are fixed and thus we know
voter preferences so that we can decide which candidate has the winning position with
respect to that issue dimension, or that, even if the candidate positions with respect to that
issue dimension are not fixed, some issues are known in advance to tend to favor one
candidate or party. For example, a presidential candidate with military experience might
be favored if defense issues were especially salient. Or, as John Petrocik (1996) has
suggested in his work on "issue ownership," one party might be widely perceived as
historically far more devoted to, say, fostering economic equality than the other, so that
claims made by the latter party that they were even more interested in achieving
economic equality would be dismissed by the voters as non-credible. Thus, the party
associated with reductions in economic equality might be favored if the issue of
economic inequality were especially salient in a campaign.
In light of such considerations we would anticipate that candidates would
compete in seeking to “activate” and make more salient those issues/issue dimensions
which they believe will favor their cause and on which their position is more popular than
that of their opponent. But, as we shall see, finding an optimal campaign strategy vis-avis issue salience can be considerably more complex.
II. Issue Salience in Two or More Dimensions
For simplicity we will present our results for two issue dimensions in which the
positioning of voter ideal points is not collinear. However, the basic results can be
generalized in a straightforward fashion beyond two dimensions.
Consider two-candidate competition over two issue dimensions. To avoid
technical complexities caused by knife-edge results such as the possibility of ties, we
assume that there are an odd number of voters and that no two voters are located at the
same point, i.e., have identical preferences. Let us imagine that, on issue 1 (the x
dimension), a majority of voters are closer to candidate B, while on issue 2 (the y
dimension), a majority of voters are closer to candidate A. The simplest such case, with
three voters, is shown in Figure 1 below, with the voters defining the vertices of the
triangle that comprises the elements of the Pareto set.
<< Figure 1 about here>>
Definition: voter preference over two or more unweighted dimensions - A voter
prefers candidate A to candidate B if that voter's total distance to candidate A is less than
the voter's total distance to candidate B on the given dimensions.
In general, if there is more than a single dimension of political competition, we
know that there will not be a stable majority equilibrium for two-candidate competition
(McKelvey, 1976, 1979). In Figure 1, the “swing” voter (in the bottom right) is closest
to candidate B, so candidate B will win. In the usual Downsian story we would now have
candidate A moving about the issue space looking for a location that will beat candidate
B. Necessarily, such a location will exist (since candidate B’s win set is non-empty).
But that new winning location for candidate A will in turn be vulnerable to a switch in
location by candidate B. Etc.
However, the notion of candidates “hopping” about the space in search of a
winning position, is very far from a realistic portrait of politics. Candidates are strongly
constrained by their past positions and history and those of their political party.2 This
means that candidates may not always be able to make a credible shift to a winning
position.
But even if candidate A in Figure 1 does not move location (perhaps because she
cannot move because her credible options are so limited that there is no location in
candidate B’s win set that is available to her), all is not lost. What candidate A can do is
to seek to manipulate the importance that voters attach to the two issue dimensions. If she
succeeds either in sufficiently inflating the importance of dimension 2 (the y dimension)
or in sufficiently diminishing the importance of dimension 1 (the x dimension), or in
doing enough of each, then candidate A, not candidate B, will have the winning position.
We can picture such changes in salience in a very straightforward geometric way
as “stretchings” or “shrinkings” of one or both issue dimensions. In Figure 2 we show
three such “salience manipulations” that are sufficient to convert candidate A’s position
into that of a winner. The first (2a) shrinks dimension 1; the second (2b) expands
dimension 2; the third (2c) does some shrinking of dimension 1 and some expansion of
dimension 2.
<< Figure 2 about here>>
Shrinking one dimension while holding the other constant is equivalent to
differentially weighting the dimensions.
Definition: voter preference over two weighted dimensions - A voter prefers
candidate A to candidate B when the horizontal distance is weighted by h and the
2
For spatial models which explicitly recognize this fact see e.g., Aranson and Ordeshook,
1972; Coleman, 1972; Wuffle et al., 1989; Owen and Grofman, 1996)
vertical distance by v if and only if the weighted total distance of the voter to candidate A
(i.e., the square root of the sum of squared x distance weighted by h and the squared y
distance weighted by v) is less than the weighted total distance to candidate B.3
While it is well known that candidates tend to emphasize the issue dimension that
favors themselves, the strategic issues involved in two-candidate competition are much
more complex than they first appear. We find that when one candidate moves the
weighting of the dimensions in the direction of placing greater (relative) weight on the
dimension in which she would receive the greatest number of votes if that were the only
dimension of choice, but does not succeed in convincing voters that this is the only
relevant dimension, increasing the weight on this dimension might actually lose votes or
even lose the election.. That is, in general, the effects of differential weighting are not
necessarily monotonic; i.e., increasing the relative weights on a particular dimension does
not necessarily consistently favor the same candidate. Indeed, we can show that under
certain conditions, increasing the weights of one dimension might increase, then
decrease, then increase, then decrease, etc. the votes given to one candidate. That makes
it very difficult in practice for candidates to campaign by attempting to increase the
weight on a dimension ) on which (if this dimension were the sole dimension of choice)
the candidate would be guaranteed a victory.
Suppose that we have two candidates, A and B, located at fixed positions in the
space. We will show that, in these circumstances, weighting of the two dimensions in
the space is equivalent to specifying the angle of a single dimension along choice is to be
made. More formally:
3
While we could present results in terms of a single parameter w, such that w was the
weight on one dimension and 1-w on the other, because we will sometimes be
considering negative weights the discussion below is easier to follow if we use separate
parameters for each of the dimensions.
Theorem 1: For two candidates, A and B, located at fixed points in the space,
which we may without loss of generality label (-x0,-y0) and (x0,y0), candidate A is
majority preferred to candidate B subject to dimensional weights of ratio h to v if and
only if candidate A is majority preferred to B along the single issue dimension defined by
the line at an angle -(h/v)(x0/y0), i.e., if and only if a majority of voter ideal points are on
the A side of the line, y = -(h/v)(x0/y0)x.
Proof of Theorem 1: Without any loss of generality, for any pair of orthogonal
dimensions, and for any points A and B, axes can be located such that the origin is at the
midpoint between A and B, and such that A is located at (-x0,-y0) and B is located at
(x0,y0). (Note that if one candidate is located below and to the left of the other, then the
first candidate is labeled A. If one candidate is below and to the right of the other, then
the situation is abstractly identical to its mirror image that can be labeled in this way.)4
Then, any given voter whose ideal point is (x, y) prefers A to B if and only if his/her
weighted distance to A is less than his/her distance to B; i.e.
h(x+x0)2 + v(y+y0)2 < h(x-x0)2 + v(y-y0)2
i.e.,
.
hx 2+2h x x0 +hx0 2 + vy 2 +2vy y0 + vy0 2 <
hx 2 - 2hx x0 +hx0 2 + vy 2 - 2vy y0 + vy0 2
i.e.,
2h x x0 +2vy y0 < - 2h x x0 - 2vy y0
i.e.
4h x x0 < - 4v y y0
4
When the position of B (x0,y0) happens to be (1,1), then this line is entirely a function of
h/v, but the proof is written for the general case of any A and B where the axes are drawn
through the midpoint between them.
Further, if we assume that y0 > 0 and v > 0 (A and B and v can always be assigned to
make this so), then the voter prefers A to B if and only if:
x<0 and y/x > - (h/v) x0/y0
or
x>0 and y/x < - (h/v) x0/y0 .
We show the geometry underlying the relevant constructions in Figure 3. The
above result implies that there exist values of h/v such that any voter on the A side of
line u would prefer A to B for those values.
<< Figure 3 about here>>
It should be apparent that being on the A side of the v line in Figure 3 is
equivalent to preferring A to B on the single dimension perpendicular to u. Similarly,
any voter on the A side of line v would prefer A for a different value of h/v and this is
equivalent to preferring A to B on a different single dimension, perpendicular to v. Thus,
it should be clear that, for two orthogonal issue dimensions, for fixed candidate locations,
every weighting, h/v , is equivalent to deciding over some single issue dimension. q.e.d.
It is easy to see from the above result that, if the vertical dimension is given a
zero weight, then the decision is determined by which candidate is closest to the median
voter along the horizontal dimension --and similarly, if the horizontal dimension is given
a zero weight, then the decision is determined by which candidate is closest to the median
voter along the vertical dimension. If the two dimensions are equally weighted, then the
candidate closest to the median voter on the dimension defined by the line passing
through both A and B is preferred by the majority.
Definition: A median line is a line such that half of the voter ideal points are on
or above the line and half are on or below the line.
Corollary to Theorem 1:
For weights of h and v, if the line y= -(h/v)(x0/y0)x is a
median line, then there is no majority preference between A and B for this particular
value of h/v. However, one candidate is majority preferred for slightly larger values of
h/v, while the other candidate is majority preferred for slightly smaller values of h/v
Proof : By definition, a median line is a line that passes through a voter ideal point
and divides the other voter ideal points in half. When the line y= -(h/v)(x0/y0)x is a
median line through the midpoint between A and B, the voter on that median line is
indifferent between A and B with the relative weights of h/v, and there is a tie among the
other voters. Increasing or decreasing the relative weights is equivalent to rotating the
dividing line between the voters preferring A from those preferring B. Therefore, rotating
from a median line one way puts the decisive voter on one side, and rotating in the
opposite direction puts the decisive voter on the other side. q.e.d.
Before we prove the next theorem we prove a needed lemma.
Lemma 1: Every point in the space is on at least one median line, and is on an
odd number of median lines
Proof:. Consider Figure 4, where p is the point of interest and the x’s represent
voter ideal points. Start with a line 0 through p, as shown.
<< Figure 4 about here >>
A majority of voter ideal points must be on one side of that line; in this case,
below the line. Call one half-space Q, and the other R. Now, rotate the line around p in a
clockwise direction, as shown in Figure 4 – the rotation to line 1 is shown. As the line
rotates, so do the half-spaces, Q and R, defined by the line. As the line passes over voter
ideal points, they switch from being part of Q to R or vice versa– in this example, moving
from line 0 to line 1 passes over one voter ideal point in the upper left, who moves then
from being part of R to part of Q.
As the rotation continues, a voter ideal point in the
lower right would move from being part of Q to part of R; etc. Once one completes a full
180 degree rotation, all of the voter ideal points that were initially part of Q have become
part of R, and vice versa. So, the number of voter ideal points in Q must go from being a
majority to being a majority as it passes some voter ideal point in the process of rotation.
The line going through that voter ideal point must be a median line, because it alone
determines which side has the majority. This proves the part of the theorem stating that
every point is on at least one median line. Now, if continuing the rotation passes over
another voter ideal point that makes Q the majority again, then the line through that point
must be another median line. However, since we know that Q must end up being the
minority half-space once the 180 degree rotation is complete, we know that every other
median line that makes it the majority again must be followed by still another median line
that makes it the minority again before the rotation is complete. Thus, there must be an
odd number of median lines passing though p.
q.e.d.
Now we can proceed to the proof of Theorem 2.
Theorem 2: For every pair of candidates, A and B, at fixed locations, there is
some weighting of the dimensions, h/v, such that A is majority preferred to B.
Proof: From Lemma 1, there must be at least one median line passing through
the origin (0,0). That median line corresponds to some (h/v). Then, from the corollary to
Theorem 1, A is majority preferred if the relative weights (h/v) are on one side (either
higher or lower) of those corresponding to that median line, and B is majority preferred
on the other side. Thus, there are relative weights that result in majority preference for A
and others that result in majority preference for B. q.e.d.
Definition: A turnover is a change in which candidate is the majority winner
accompanying a change in the relative weights attached to the two dimensions.
Theorem 3: For every pair of candidates, A and B, at fixed locations, changes in
weightings give rise to an odd number of turnovers, with one turnover for each median
line passing through the midpoint between A and B.
Proof : As shown in the proof of Theorem 2, as, say, the weighting increases on h
relative to v, A gains some voters, then loses others. This pattern of gains and losses
continues as we further increase h relative to v. The actual majority changes from one
candidate to the other each time the rotating line crosses a median line. Thus, there will
be as many switches as there are median lines passing through the midpoint between A
and B. But there are an odd number of median lines through any point.
q.e.d.
While we have shown that, for any set of voter ideal points and any two
candidates, A and B, and any set of coordinates defining orthogonal dimensions, one can
find a set of weights such that if each voter votes for the candidate whose weighted
distance is closer to that voter, candidate A (or B) will get a majority of votes, Theorem 3
has direct implications for whether each candidate can pursue the simple strategy of
persuading voter to increase the relative weights attached to the dimension or dimensions
on which they would see themselves as favored. Such a simple strategy exists only when
a candidate's vote share monotonically increases as the relative weight attached to a
dimension on which his is the winning position increases. But often such monotonicity is
absent. Indeed, there are circumstances in which increasing the relative weight attached
to, say h (i.e., increasing the ratio h/v) can first shift a candidate from winning to losing,
then from losing to winning, then from winning to losing, etc.. In other words, even if a
particular dimension favors a particular candidate, attempts by that candidate to get
voters to weight that dimension more heavily may backfire because, for some increases in
the weighting of that dimension, the candidate will actually be disadvantaged rather than
advantaged! Thus candidates may have trouble effectively pursuing a strategy about the
appropriate dimensional weighting that will unequivocally improve his vote share if
voters move only some of the way (but not all the way) toward that weighting (or
overshoot it) is one of the key results in our paper.
However, there is one further complication we now need to discuss. While it is
true that, as we have shown above, there are as many majority turnovers as there are
median lines through the midpoint of A and B, and (since there is always at least one
such median line) there is always at least one turnover, some of these turnovers can
occur only if we assign a negative weight to one of the dimensions. But, when the axes
are fixed, then negative weightings should be regarded as infeasible. Weighting a
dimension negatively means that a voter prefers a candidate who is further from the voter
on that dimension. That is not consistent with our common sense assumption that voters
prefer candidates whose views are like their own.
If we fix the set of issue dimensions and rule out negative weightings, the
strategic situation may be simplified in that the exclusion of certain potential turnovers
as infeasible (those associated with negative weights) may mean that one of the
candidates may never be able to get a majority in any feasible weighting scheme.
Alternatively, if we rule out negative weighting, there may now only be a single feasible
turnover. If there is only a single feasible turnover, then one candidate should have the
simple optimal strategy of seeking to increase the relative weight given by voters to one
of the dimensions, while the other candidate has the equally clear strategy of seeking to
reduce the weight given by voters to that issue dimension.
Theorem 4: One candidate is majority preferred to the other for all feasible (nonnegative) weights if and only if the only median lines that pass through the midpoint
between A and B are contained entirely within the upper right and lower left hand
quadrants.
Proof: The previous proofs have shown that thereis a turnover where and only
where there is a median lines corresponding to the line,
y= -(h/v)(x0/y0)x.
The weights are not feasible when h/v < 0; that corresponds to a line through the origin
with positive slope; i.e. going through the lower left and upper right quadrants. If all the
median lines go through those quadrants, then there are no median lines based upon
feasible weights, and there are no feasible turnovers. With no turnovers, the same
candidate must get the majority for all feasible weights.
q.e.d.
Definition: For a given set of voter ideal points, the yolk is the smallest circle
intersecting all median lines (Mckelvey,1986; Miller, Grofman and Feld, 1990).
Corollary 1 to Theorem 4: (a) If the yolk is located entirely within the upper-right
(lower-left) quadrant, then A (B) is majority preferred for all feasible weights, i.e., there
are no feasible turnovers. (b) If the yolk is located entirely within the lower-right
(upper-left) quadrant, then A is majority preferred on one dimension, and B is majority
preferred on the other. In this case there is always at least one feasible turnover and the
number of turnovers must be odd.
Proof: (a) If the yolk is located entirely within the upper-right (lower-left)
quadrant, then since all median lines go through the yolk, the only median lines that can
go through the midpoint between A and B must only go through the upper-right and
lower-left quadrants. From Theorem 4, we must have the same candidate winning
irrespective of the weights. If the yolk is in the upper-right (lower-left), then A (B)
always wins (is on the midpoint side of the median line.
(b) Since all median lines pass through the yolk, then all median lines passing
through the midpoint between A and B must also pass through the yolk and therefore go
through the upper-left and lower-right quadrants. There is always at least one median
line and an odd number of such median lines through this midpoint, and each median line
switches the majority winner. q.e.d.
Definition: An issue salience monotonicity paradox arises when there exist
feasible values of h/v, such that increases in the ratio h/v change the majority preference
from A to B, and other feasible values of h/v such that increases in the ration h/v change
the majority preference from B to A.
Corollary 2 to Theorem 4: There is an issue salience monotonicity paradox if and
only if there are two or more median lines through the origin (the midpoint between A
and B) that pass through the upper left and lower right quadrants.
Corollary 3 to Theorem 4: If one candidate is majority preferred on one issue
dimension while the other candidate is preferred on the other, we avoid an issue salience
monotonicity paradox if and only if there is only one median line through the origin that
passes through the upper left and lower right quadrants.
Definition: A simple issue salience paradox occurs when one candidate wins on
both of the two issue dimensions, but loses for some particular feasible weighting of
those dimensions.
Corollary 4 to Theorem 4: A simple issue salience paradox occurs if and only if
there are an even number of median lines passing through the origin that goes through
the upper left and lower right quadrants.
Proof: An even number of median lines passing through the origin that goes
through the upper left and lower right quadrants implies an even number of turnovers.
Thus, the candidate who is majority preferred on one dimension is turned over and back
(perhaps multiple times). q.e.d.
So far , we have considered what happens if we treat axes as fixed and also what
happens if we rule out negative weights. But, if candidates can manipulate choice of the
axes as well as the weights to be attached to each, then, in effect, all weights become
feasible, and Theorem 2 applies.
Theorem 5: For every pair of candidates, A and B, at fixed locations, there exist
some set of orthogonal dimensions and some set of non-negative weights on the distances
in those dimensions such that A (B) is majority preferred to B (A) .
Proof: There is always at least one median line through the midpoint between A
and B. If the axes are rotated so that median line passes through the feasible
quadrants, then there are weights that switch the majority preferred candidate at that
median line. On one side, A is preferred to B; on the other, B is preferred to A. q.e.d.
The implication of Theorem 5 is that, even with fixed candidate positions, and
even where there is an initial set of dimensions such that there are no feasible weights by
which candidate A can be majority preferred to candidate B, there is still always some
new set of axes and some set of relative weights for those new axes that result in
candidate A receiving a majority of votes. Of course, we would expect that it would
ordinarily be very difficult for a candidate to simultaneously persuade voters about both
the need to redefine the dimensional axes and about the relative weights which should be
given each dimension. Still, such two-pronged heresthetic communications have, at least
in principle, the potential for converting a loser into a winner.
Discussion
The standard Downsian approach to candidate/party competition emphasizes
party/candidate location as the driving force in voter choice, with voters choosing the
issue platform closest to the voter's own ideal point. But, often the location of candidates
will be, if not completely fixed, at least constrained, with only so much "wiggle room."5
Here, paralleling ideas in Petrocik (1996) on "issue-ownership," we have looked at
situations in which certain issues favor a particular party or candidate. We have offered a
widened notion of strategic choice, in which candidate decisions go beyond the choice of
a policy platforms to include decisions about persuasive aspects of the campaign -- here,
which dimensions to emphasize. In such situations, we have looked at the consequences
of attempts to persuade voters to change the relative importance that they attach to
different issues, taking the candidate issue positions as (largely or entirely) given.
There are many ways in which candidates and their supporters can seek to change
the salience of different issues and thus to affect voter choices. For example, Salvanto
(2000) has looked at the effects of ballot referenda in California on voter perceptions of
the most relevant campaign issues. His analyses look both at the anticipated
consequences of decision to place particular referenda on the ballot and on the decisions
of some candidates to identify their own campaigns with particular ballot issues, a
practice he call “referenda as running mates.” In California in 1994, the incumbent
Republican governor, Pete Wilson, ran on anti-illegal-immigration platform and strongly
associated his campaign with the campaign to pass Prop. 187, a referenda proposing to
eliminate state spending on public services for illegal immigrants. By associating himself
with a YES vote on the referendum he increased the salience of the immigration issue for
those voting on the governor's race.
While this strategy appeared to make sense for Wilson, in that a substantial
majority of voters were in favor of Prop. 187, the results in this paper show that we must
be cautious in assuming that being associated with the winning side of an issue
necessarily benefits a candidate as the (relative) weight attached to that issue increases
among voters. There is the potential for loss of support when voters increase the weight
attached to a dimension on which a candidate is favored, even though the candidate
would win if that were the only dimension of choice.
The knowledgeable reader may have noticed that our results about the
nonmonoticity of changes in dimensional weightings seem to be similar in spirit to results
about cycling in the absence of a core point. But, we must be careful. Even with a core
when issues are weighted equally, differential weighting of issue dimensions can change
the outcome. This paper is, we believe, the first to have shown specifically how, given
the geometry of voter choice, perverse effects of dimensional weightings can arise.
5
Cf. Wuffle et al. (1989).
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Figure 1
A Three Voter Example With
Candidate B as the Winner
B
A
Figure 2
The Same Three Voter Example as in Figure 1
Now Stretched and/or Shrunk to Make Candidate
A the Winner
B
A
B
(a)
B
A
A
(b)
(c)
Figure 3