Análisis de la causalidad de incendios forestales período 2008-2018

In order to assess the rate of correct voting (CV) among an electorate, we first must consider how to measure CV as pertains to voter preferences for attributes (e.g. policies). To do this, we ask voters for their preferences on a variety of policy issues, and match those with the positions of the political alternatives on offer- much as voters (should) do when voting. Arguments over the two dominant ‘spatial’ models of voting, ‘proximity’

(Davis & Hinich, 1966; Downs, 1957) and ‘directional’ (MacDonald, Listhuag, & Rabinowitz, 1991;

Rabinowitz & MacDonald, 1989), abound in political science and public policy (Blais et al., 2001; Cho &

Endersby, 2003; Lewis & King, 1999), with attempts at unifying the two under a common framework (Merril

& Grofman, 1999; Weber, 2015).

Proximal Model: The ‘proximity spatial’ model is the most prominent spatial theory of electoral choice (Downs, 1957), positing electoral choice is best understood by examining the proximity between

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candidate/party attributes and voters’ preferences; simply, voters will choose candidates whose preferred policies are ‘closer’ to theirs. The proximity model has a lot of appeal, and similarities to decision-science:

individuals (voters) make decisions (choosing candidates) according to their preferences (proximity between policy positions). It presents a “simple and intuitive link between formal representation of voters’ issue-based information processing and their observable candidate-based electoral choice” (Ye, Li, & Leiker, 2011, p.

497).

Within the proximity model, we define a multi-dimensional policy space (‘Davis-Hinich space’; Davis &

Hinich, 1966) where a voter’s most preferred policy bundle, and their perception of candidates’ issue positions, are represented by points in the space; their respective ‘ideal points’. The spatial distance between these ideal points corresponds to preference proximity: smaller distance, the more proximate the preferences. Preference proximity helps explain individual voters’ comparison of candidates: a voter ranks candidates in accordance with the distance from their respective ideal points, such that the most proximate is the most preferred and so forth.

Proximal CV Method: Our ‘proximal’ of correct voting arises from the standard Euclidian distance formula for calculating the distance between 2-points in an n-dimensional space, and is standard in the ‘proximal model’

of voter decision-making used by the political sciences (Hinich & Enelow, 1984). The resulting output is a utility score for each candidate, relative to the voter’s stated preferences, and is illustrated in Equation 1; where q is a candidate’s score on a given issue and p is a voter’s self-placement on the issue, over N policy issue dimensions. Decision-weights (dw) are derived from participants’ explicit ratings of a policy issue’s importance to them, obtained via a questionnaire post-experiment, and rescaled to range between ‘0’ and ‘1’.

Equation 1: Proximal Correct voting, using a Euclidian distance equation (with decision weights).

Where participants indicated a decision-weight of ‘0’, or answer ‘Don’t Know’ on a policy issue questionnaire, this dimension is removed from the equation, as if we multiply any dimension by a dw of 0,

𝑑 𝑞, 𝑝 = 𝑞₁− 𝑝₁ ² 𝑑𝑤₁ + 𝑞₂− 𝑝₂ ² 𝑑𝑤₂ … + 𝑞_𝑛− 𝑝_𝑛 ² 𝑑𝑤_𝑛 = 𝑞_𝑖−𝑝_𝑖 ² 𝑑𝑤_𝑖

𝑛 𝑖=1

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then this will be incorrectly scored as being perfectly aligned with a candidate on that policy issue, and will result in a biased score.

We prefer the proximal model and methods of operationalizing correct voting, as lab and survey experiments by Claassen (2007), Tomz and Van Houweling (2008) and Lacy and Paolino (2010) find that proximity theory offers the best model of voting behavior. We outline additional reasons for our use of the proximity model below. First, we review the directional model, as favoured by Lau and Redlawsk (1999;

2006).

Directional Model: The Rabinowitz and MacDonald (1989) ‘directional spatial’ model states that the distance between a voter and a candidate on any given dimension (e.g. policy issue) matters less than whether or not they are on the same ‘side’ on an issue (i.e. on the same side, relative to the ‘neutral point’ of an issue).

Rabinowitz and MacDonald (1989) argue this captures the ‘affective intensity’ of spatial issue voting, which is missed from the proximity model. The authors state that, if a candidate and voter are on the ‘same side’ the affect associated with the issue will be positive (regardless of distance); whereas if they are on ‘opposite sides’

of an issue, affect will always be negative (regardless of distance). Thus the utility of a candidate on a given dimension for a voter can be expressed formally in Equation 2, where U(Qj) is the utility of candidate Q over all ideal vector points in the dimension j, for a voter with a vector of ideal points Pi, where P0 is the neutral point.

Equation 2: Directional spatial model of voting.

Simply stated; the utility for any given candidate is the product of the distance of a candidate from the neutral point and the distance of a voter from the neutral point, on a given dimension.

Directional CV Method: Determining a ‘standard’ operationalisation of Lau and Redlawsk’s ‘directional’

measure of correct voting is mildly difficult, as they use differing methodologies when examining CV in laboratory settings (Lau & Redlawsk, 1997; 2006), or determining CV from national election panel surveys like the American National Election Survey (ANES; Lau, Andersen, & Redlawsk, 2008). Despite this, at the core of their directional measure(s), is the Rabinowitz and MacDonald (1989) directional spatial model.

U 𝑄_𝑗 = Q_𝑗 − P₀ ′(P_𝑖− P₀)

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Using the directional model of voting, Lau and Redlawsk (1999; 2006) aim to capture a voter’s ‘agreement’

with (or ‘favourability’ toward) a candidate on a given dimension. They further rescale the resulting utility score to range between +/- 1 for a given candidate on a given dimension, based on the maximum range possible from the neutral-point. For example, for a 7-point scale where ‘4’ is the midpoint (or ‘neutral-point’), the maximum range from the neutral point is -3 and +3, whose absolute product is ‘9’. A scenario where a voter and candidate occupy the extreme ends on an issue scale would result in a utility of -1 for that issue (i.e. [[7-4] * [1-[[7-4]]/9 = -1]. Lau and Redlaswk (2006) average this utility over the number of items accessed for a given candidate.

It is also important to look at what dimensions are included in constructing the measure(s) as per Lau and Redlawsk (2006; Lau et al., 2008). In calculating their directional measure of correct voting, Lau et al. (2008) include “the interests and concerns of each voter” (p. 408) by including some, but not always all, of the following: a measure of party identification (strength); trait judgments of candidate personality; thermometer ratings of candidate-group links; candidate performance evaluations (if examining existing datasets from the ANES); and issue stands (where voters line on certain policy issues). All these dimensions are rescaled to range between -/+ 1.

Secondly, Lau et al. (1997; 2008) state they include the degree a voter ‘cares’ about each of these dimensions of judgment: by obtaining explicit weights (e.g. a participant reporting their partisan identification); or calculating implicit weights (e.g. the proportion of questions answered for a judgment dimension, a proxy for how much a participant ‘cares’ about that dimension). They calculated policy issue weights either by asking for participants’ perceived importance of that issue to them (Lau & Redlawsk 1997), or by calculating a scaled importance weight for each issue based on how many candidates in the choice set they attributed a perceived position to; ‘0’ if unanswered, ‘0.5’ if answered at all, and increasing the weight proportionately towards ‘1’ with each additional candidate the voter attributed a position to on that policy issue.

Lau et.al (2008) calculated 4 different versions of their directional measure; by using (un)weighted versions of either an additive or averaged utility model for each candidate, noting that these measures are highly correlated and “there were absolutely no differences between the additive and averaging algorithms for

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combining the information”, and “while it is certainly possible to create situations where these two procedures produce very different results, in practice those situations apparently do not occur very often” (Lau et al., 2008, p.401).

We construct our own version of Lau and Redlawsk’s (2006; 2008) directional (utility) measure, in order to check if using a ‘directional spatial model’ vs. a ‘proximal spatial model’ approach leads to different conclusions around ‘correct voting’ in our own experiments. As Lau et al. (Note 37, 2013) state that empirically the results arising from the two are usually indistinguishable, we do not expect to observe any. Additionally, Weber (2015) notes the high collinearity of both model predictions, stating that while the models are theoretically distinct, they make identical predictions in most real-world situations. Further details on the measure can be found in Appendix B.