By Yeaton Muelas Gil
We shall start by looking at an example from a news report informing on a group of researchers from Spain who developed a virtual coach to prevent depression with the headline:
Médicos salmantinos crean un entrenador virtual que previene la depresion laboral (La Gaceta, 10/04/2021. Page 4)
[Doctors from Salamanca create a virtual coach that prevents depression at work]
If only the translation is observed, there is no indication of the gender of the doctors and researchers involved in the project; however, such gender is indicated in the original version (namely, the masculine generic). The difference simply comes from the way the English and Spanish languages indicate (or not) gender in their system: while the former is what is called a natural gender language, where most role nouns are not morphologically marked, the latter is a grammatical gender language, where nouns are usually marked for gender and therefore carry an additional cue to referential gender (Reali 2015). In other words, while the Spanish language indicates the gender of words by means of an ending vowel (mainly -o for masculine, -a for feminine), there is no such marking in English.
While this may seem a simple linguistic norm, it is of great importance for linguistic studies. When more than one gender is involved in a communicative or discursive situation in Spanish, or the gender is unknown or irrelevant, the Real Academia de la Lengua Española states that the masculine generic shall be used and is equally inclusive of all genders. However, many studies have proved that the use of the masculine generics inherently implies a lower depiction and projection of women in all situations. Scholars have recently investigated the consequences of using it in comparison to other more inclusive alternatives, such as the double form with a slash (médicos/as), the complete form of feminine and masculine gender (médicas y médicos) or even emerging options like the vowel -e or the consonant -x.
With the intention of continuing this line of research, a preliminary behavioral study was carried out to confirm whether participants do project a higher proportion of women when using the alternative forms in comparison to the normative one. Thus, 117 university students used a Likert scale to rate a list of 60 jobs as “mainly male” or “mainly women”; there were 3 different options of the survey, all containing the same jobs but presented in a different form (survey A: médicos, survey B: médicos/as; survey C: médicas y médicos) and each participant would only answer one of the options.
The results of this preliminary study show two main outcomes: there is a trend in general that shows how more women are in fact included in the scale when the job is presented in the alternative forms, compared to the masculine generic option; moreover, this trend is reversed for the jobs which are stereotypically female in society (such as hairdresser, nurse, nanny, etc.), meaning fewer women (or more men) are included in the alternative forms. This seems to agree with and confirm the previous studies claiming that the use of inclusive language reduces the stereotype regardless of which gender is involved, and therefore should be used if the gender gap is to be more widely or easily accepted.
Still, these preliminary results obtained in the behavioral study were nonetheless limited to a small part of the Spanish population. For the purpose of this subject and this project, the present study applies the Rational Speech Act (RSA) framework to this problem and builds the semantics into a computational model that aims at confirming the aforementioned trend. The objective is not only to compare behavioral with computational results and therefore achieve a stronger statement, but also to be able to provide a more general, applicable, justified and comparable model. __
Our model is built on the foundations of the model of generic language covered in Chapter 7. We extend this model to address the issue of inferring the prevalence of women among a group of professionals in order to see whether the RSA can account for the observed behavioral effects, or whether some other mechanism must be in play. We lay out the architecture of the model below, building up.
NB: For the purposes of this project, we assume that all group members are drawn from the man/woman binary. We operationalize this accordingly by treating the observed prevalence as the percent of women in the group. The percent of men in the group can therefore be inferred as 1 minus the observed prevalence of women.
Whereas the previous generics model had only two utterances (generic and null), we define four possible utterances:
mascpl: masculine plural – the so-called defaultmslashf: masculine/feminine (e.g.: médicos/médicas) which is much higher cost than mascpl but can be applied to the same groupsfem: feminine plural – theoretically licensed only when the group contains exactly zero men (but we relax this condition as shown below)uttnull: the null utterance (silence)The costs are shown in the code block below. mascpl and uttnull have the same low cost of 1 while the fem utterance is less frequent and therefore higher cost (4) and the higher effort mslashf utterance has a cost of 6.
We define the utterance prior as a uniform draw from our four utterances.
// Possible utterances
var utterances = ['mascpl', 'mslashf','fem','uttnull']
// Utterance costs
var cost = {
'mascpl': 1,
'mslashf': 6,
'fem': 4,
'uttnull': 1
}
// Utterance prior
var utterancePrior = function() { return uniformDraw(utterances) }
Infer(utterancePrior)
With the exception of the null utterance (which always returns true), the truth value of each of our utterances is defined according to some thresholds thresholdM or thresholdF. The parameters for these thresholds are currently rather arbitrary, with thresholdM doing a uniform draw from the threshold bins (also more or less arbitrary), and thresholdF drawing from the same bins (for more discussion on this distribution, see here). In the future, we hope to estimate these thresholds empirically, but given the speaker intuition that the threshold for a fem utterance must be near 1, we provide a potential parameterization of this distribution with a relatively high concentration of 50 and a mean of 0.85, but for the purposes of simplicity, we use the same prior for both thresholdM and thresholdF.
We then define the truth conditions for the mascpl utterance as true when the observed prevalence is less than or equal to thresholdM. In the same way, fem is true when the observed prevalence is greater than or equal to thresholdF. The truth value of our high-cost mslashf utterance is defined as true when the observed prevalence is either less than or equal to thresholdM or greater than or equal to thresholdF–the disjunction of the other two utterances. A previous version used strictly greater than or less than operations for this utterance, but using the greater than or equal to or less than or equal to operators does not seem to meaningfully impact the results.
Our meaning function therefore looks up the conditions based on the utterance and returns the corresponding truth value.
// Threshold for using the masc utterance
var thresholdPriorM = function() { return uniformDraw(thresholdBins) }
// Threshold for using the fem utterance
// var thresholdPriorF = function() { sample(DiscreteBeta(0.85,50)) }
// Meaning functions by utterance
var uttFns = {
uttnull : function(){return true},
mascpl : function(prevalence,thresholdM,thresholdF){return prevalence <= thresholdM},
mslashf : function(prevalence,thresholdM,thresholdF){return prevalence >= thresholdF
|| prevalence <= thresholdM},
fem : function(prevalence,thresholdM,thresholdF){return prevalence >= thresholdF} // all women
}
// Select relevant meaning function
var meaning = function(utterance, prevalence, thresholdM,thresholdF) {
var uttfn = uttFns[utterance]
return uttfn(prevalence,thresholdM,thresholdF)
}
We then incorporate this into the prior model from Chapter 7 on generics. Whereas in that model, the prior was a mixture of both a stable and unstable distribution, we need only the stable distribution– essentially what proportion of people in that profession are women. This prior distribution is drawn from a discretized Beta distribution with mean prevalence, and a constant concentration of 20. We hope to more accurately fit this concentration parameter by profession in future versions.
For the purposes of this paper, we selected three exemplar professions:
Prevalence is indicated as percent women. A prevalence of 0 would indicate all men, prevalence of 1 would indicate all women. We will sometimes intermix this by making reference to the prevalence of men going up which would simply be 1 - prevalence.
// Prior model
// Modified from Ch. 7 Generics for stable distribution only
var priorModel = function(params){
Infer({model: function(){
var g = params['prevalenceWhenPresent']
var d = params['concentrationWhenPresent']
var StableDistribution = DiscreteBeta(g, d)
return sample(StableDistribution)
}})
}
// Prevalence when present for representative professions
var professions = {camio: {prevalence: .21}, // truck driver
medic: {prevalence: .51}, // doctor
peluq: {prevalence: .79}} // hairdresser
// Get profession from lookup table
var prof_lookup = function(job){
return professions[job]
}
// Query a profession and get the prevalence when present
var prof = 'peluq'
var prof_params = prof_lookup(prof)
// Define prior for a profession
var prior = priorModel({
prevalenceWhenPresent: prof_params.prevalence,
concentrationWhenPresent: 20
})
Our literal listener $L_0$ is based on the $L_0$ from Chapter 7. As arguments it takes an utterance, a prior model of the prevalence for a profession (statePrior), and two thresholds corresponding to the prevalence of men required to trigger a mascpl utterance (thresholdM), and to the prevalence of women required to trigger a fem utterance (thresholdF). Given these elements, the listener performs a uniform draw from the discrete bins of the prior distribution. It then checks whether the observed utterance is consistent with that prevalence and the two given thresholds, and returns a truth value. If the meaning function returns true, then the listener returns the prevalence.
// Literal listener (L0)
// cf. Ch. 7 Generic Language
var listener = function(utterance, statePrior,thresholdM,thresholdF) {
Infer({model: function(){
var prevalence = uniformDraw(bins)
var m = meaning(utterance, prevalence, thresholdM,thresholdF)
condition(m)
return prevalence
}})
}
We provide a basic demonstration of the $L_0$ behavior below.
// Literal listener behavior
// Bins
var bins = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1]
var thresholdBins = [0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9]
// function returns a discretized Beta distribution
var DiscreteBeta = cache(function(g, d){
var a = g * d, b = (1-g) * d;
var betaPDF = function(x){
return Math.pow(x, a-1)*Math.pow((1-x), b-1)
}
var probs = map(betaPDF, bins);
return Categorical({vs: bins, ps: probs})
})
var priorModel = function(params){
Infer({model: function(){
var g = params['prevalenceWhenPresent']
var d = params['concentrationWhenPresent']
var StableDistribution = DiscreteBeta(g, d)
return sample(StableDistribution)
}})
}
// Possible utterances
var utterances = ['mascpl', 'mslashf','fem','uttnull']
// Utterance costs
var cost = {
'mascpl': 1,
'mslashf': 6,
'fem': 4,
'uttnull': 1
}
// Utterance prior
var utterancePrior = function() { return uniformDraw(utterances) }
// Meaning functions by utterance
var uttFns = {
uttnull : function(){return true},
mascpl : function(prevalence,thresholdM,thresholdF){return prevalence <= thresholdM},
mslashf : function(prevalence,thresholdM,thresholdF){return prevalence >= thresholdF
|| prevalence <= thresholdM},
fem : function(prevalence,thresholdM,thresholdF){return prevalence >= thresholdF} // all women
}
// Select relevant meaning function
var meaning = function(utterance, prevalence, thresholdM,thresholdF) {
var uttfn = uttFns[utterance]
return uttfn(prevalence,thresholdM,thresholdF)
}
// Prior model
// Modified from Ch. 7 Generics for stable distribution only
var priorModel = function(params){
Infer({model: function(){
var g = params['prevalenceWhenPresent']
var d = params['concentrationWhenPresent']
var StableDistribution = DiscreteBeta(g, d)
return sample(StableDistribution)
}})
}
// Prevalence when present for representative professions
var professions = {camio: {prevalence: .21}, // truck driver
medic: {prevalence: .51}, // doctor
peluq: {prevalence: .79}} // hairdresser
// Get profession from lookup table
var prof_lookup = function(job){
return professions[job]
}
// Literal listener (L0)
// cf. Ch. 7 Generic Language
var listener = function(utterance, statePrior,thresholdM,thresholdF) {
Infer({model: function(){
var prevalence = uniformDraw(bins)
var m = meaning(utterance, prevalence, thresholdM,thresholdF)
condition(m)
return prevalence
}})
}
// Query a profession and get the prevalence when present
var prof = 'peluq'
var prof_params = prof_lookup(prof)
// Define prior for a profession
var prior = priorModel({
prevalenceWhenPresent: prof_params.prevalence,
concentrationWhenPresent: 20
})
// Run literal listener
listener('mslashf',prior,.5,.5)
Given the high-cost mslashf utterance and a prior model for peluq (hairdresser), and equal values for thresholdM == thresholdF == 0.5, the listener produces a bimodal distribution estimating the prevalence of women among peluqueros/as to be either around 0.2 or around 0.8. This bimodal distribution makes sense given the disjunction logic used in the semantics for this utterance.
Our speaker, too, is based on the speaker from the generics model in Chapter 7, but modified in a crucial way. The original speaker would draw an utterance, and return the log odds of that utterance and prevalence under the literal listener. The utterance cost is then subtracted from these log odds, and the result is multiplied by the speaker optimality parameter alpha and returned.
Whereas in the original generics model, the costs of the utterances were constant, we now weight cost by strength of stereotype, i.e.: utterances used to describe states near the extremes (0 or 1) are costlier than utterances used to describe states near 0.5. We operationalize this by introducing strength which takes the absolute value of the prevalence - 0.5 such that prevalence values near 0 or 1 will produce strength values close to 0.5, and prevalence values near 0.5 will produce strength values near 0.
This new strength value is then multiplied by the utterance’s cost, thus amplifying utterance cost more at the periphery.
// Speaker (S)
var alpha = 4
// Modified from Ch. 7 Generics to weight cost by stereotype strength
var speaker = function(prevalence, statePrior,thresholdM,thresholdF){
// get strength of stereotype
var strength = Math.abs(prevalence - 0.5)
Infer({model: function(){
var utterance = utterancePrior();
var L = listener(utterance, statePrior, thresholdM,thresholdF);
// factor( alpha * (L.score(prevalence) - cost[utterance] ))
factor( alpha * (L.score(prevalence) - (cost[utterance] * strength) ) )
return utterance
}})
}
We provide a basic demonstration of $S$ behavior below.
// Speaker behavior
// Bins
var bins = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1]
var thresholdBins = [0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9]
// function returns a discretized Beta distribution
var DiscreteBeta = cache(function(g, d){
var a = g * d, b = (1-g) * d;
var betaPDF = function(x){
return Math.pow(x, a-1)*Math.pow((1-x), b-1)
}
var probs = map(betaPDF, bins);
return Categorical({vs: bins, ps: probs})
})
var priorModel = function(params){
Infer({model: function(){
var g = params['prevalenceWhenPresent']
var d = params['concentrationWhenPresent']
var StableDistribution = DiscreteBeta(g, d)
return sample(StableDistribution)
}})
}
// Threshold for using the masc utterance
var thresholdPriorM = function() { return uniformDraw(thresholdBins) }
// Threshold for using the fem utterance
var thresholdPriorF = function() { sample(DiscreteBeta(0.85,50)) }
// Possible utterances
var utterances = ['mascpl', 'mslashf','fem','uttnull']
// Utterance costs
var cost = {
'mascpl': 1,
'mslashf': 6,
'fem' : 4,
'uttnull': 1
}
// Utterance prior
var utterancePrior = function() { return uniformDraw(utterances) }
// Meaning functions by utterance
var uttFns = {
uttnull : function() {return true},
mascpl : function(prevalence,thresholdM,thresholdF) {return prevalence <= thresholdM},
mslashf : function(prevalence,thresholdM,thresholdF) {return prevalence > thresholdF || prevalence < thresholdM},
fem : function(prevalence,thresholdM,thresholdF) {return prevalence >= thresholdF} // all women
}
// Select relevant meaning function
var meaning = function(utterance, prevalence, thresholdM,thresholdF) {
var uttfn = uttFns[utterance]
return uttfn(prevalence,thresholdM,thresholdF)
}
// Prior model
// Modified from Ch. 7 Generics for stable distribution only
var priorModel = function(params){
Infer({model: function(){
var g = params['prevalenceWhenPresent']
var d = params['concentrationWhenPresent']
var StableDistribution = DiscreteBeta(g, d)
return sample(StableDistribution)
}})
}
// Prevalence when present for representative professions
var professions = {camio: {prevalence: .21}, // truck driver
medic: {prevalence: .51}, // doctor
peluq: {prevalence: .79}} // hairdresser
// Get profession from lookup table
var prof_lookup = function(job){
return professions[job]
}
// Literal listener (L0)
// cf. Ch. 7 Generic Language
var listener = function(utterance, statePrior,thresholdM,thresholdF) {
Infer({model: function(){
var prevalence = uniformDraw(bins)
var m = meaning(utterance, prevalence, thresholdM,thresholdF)
condition(m)
return prevalence
}})
}
var alpha = 4;
// Speaker (S)
// Modified from Ch. 7 Generics to weight cost by stereotype strength
var speaker = function(prevalence, statePrior,thresholdM,thresholdF){
// get strength of stereotype
var strength = Math.abs(prevalence - 0.5)
Infer({model: function(){
var utterance = utterancePrior();
var L = listener(utterance, statePrior, thresholdM,thresholdF);
// factor( alpha * (L.score(prevalence) - cost[utterance] ))
factor( alpha * (L.score(prevalence) - (cost[utterance] * strength) ) )
return utterance
}})
}
// Query a profession and get the prevalence when present
var prof = 'peluq'
var prof_params = prof_lookup(prof)
// Define prior for a profession
var prior = priorModel({
prevalenceWhenPresent: prof_params.prevalence,
concentrationWhenPresent: 20
})
var thresholdM = 0.5 //thresholdPriorM()
var thresholdF = 0.5 //thresholdPriorF()
var prev = 0.3 //uniformDraw(bins)
display(prev)
speaker(prev,prior,thresholdM,thresholdF)
Given thresholdM = thresholdF = 0.5 and a prevalence = 0.7 > 0.5, the speaker will assign the most mass (~50%) to the fem utterance with marginally less given to uttnull and a tiny bit to the high-cost mslashf. The mascpl utterance is incompatible with the literal semantics in this case. If we take a prevalence = 0.3 < 0.5, then a markedly different pattern is observed. The speaker assigns more than 90% of posterior mass to the mascpl, with less than 10% assigned to uttnull and a negligible amount assigned to mslashf. The fem utterance is incompatible with the literal semantics here.
Importantly, under these conditions for the speaker and literal listener, there is no state where the mslashf utterance is favored.
We base our Pragmatic listener ($L_1$) on the pragmatic listener from the Chapter 5 vagueness model. Whereas in that case, the $L_1$ was trying to infer the speaker’s threshold for “expensiveness” and an item’s true price, here the $L_1$ is attempting to infer the speaker’s thresholdM and thresholdF values, as well as the true prevalence of women among the group of professionals that the speaker is talking about.
The pragmatic listener first draws a sample from its prior model for that profession, and then samples a thresholdM and a thresholdF which are passed to the speaker which returns the log odds for the observed utterance under that prevalence and those thresholds. The pragmatic listener then returns a 3-tuple object which contains the estimated prevalence and the two thresholds.
// Pragmatic listener (L1)
// Modified from Ch. 5 Vagueness
var pragmaticListener = function(utterance,prior) {
// run inference
return Infer({method: 'enumerate'},
function() {
var prevalence = sample(prior)
var thresholdM = thresholdPriorM()
// var thresholdF = thresholdPriorF()
var thresholdF = thresholdPriorM()
factor( speaker(prevalence, prior,thresholdM,thresholdF).score(utterance) );
return { prevalence: prevalence ,thresholdM: thresholdM, thresholdF: thresholdF};
});
};
As we incorporate the pragmatic listener, we now have a complete model which will infer the prevalence of women in some professional group based on its priors for that profession and its knowledge of the possible utterances.
Below, we run a simulation over the three professions (truck driver – camio, doctor – medic, hairdresser – peluq) for two of the possible utterances: the “default” mascpl utterance, and the higher-cost mslashf utterance.
// Put it all together
// Bins
// var bins = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1]
// var thresholdBins = [0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9]
// discretized range between 0 - 1
var bins = map(function(x){
_.round(x, 2);
}, _.range(0.01, 1, 0.05));
var thresholdBins = map2(function(x,y){
var d = (y - x)/ 2;
return x + d
}, bins.slice(0, bins.length - 1), bins.slice(1, bins.length))
// function returns a discretized Beta distribution
var DiscreteBeta = cache(function(g, d){
var a = g * d, b = (1-g) * d;
var betaPDF = function(x){
return Math.pow(x, a-1)*Math.pow((1-x), b-1)
}
var probs = map(betaPDF, bins);
return Categorical({vs: bins, ps: probs})
})
var priorModel = function(params){
Infer({model: function(){
var g = params['prevalenceWhenPresent']
var d = params['concentrationWhenPresent']
var StableDistribution = DiscreteBeta(g, d)
return sample(StableDistribution)
}})
}
// Threshold for using the masc utterance
var thresholdPriorM = function() { return uniformDraw(thresholdBins) }
// Threshold for using the fem utterance
var thresholdPriorF = function() { sample(DiscreteBeta(0.89,30)) }
// Possible utterances
var utterances = ['mascpl', 'mslashf','fem','uttnull']
// Utterance costs
var cost = {
'mascpl': 1,
'mslashf': 6,
'fem': 4,
'uttnull': 1
}
// Utterance prior
var utterancePrior = function() { return uniformDraw(utterances) }
// Meaning functions by utterance
var uttFns = {
uttnull : function() {return true},
mascpl : function(prevalence,thresholdM,thresholdF) {return prevalence <= thresholdM},
mslashf : function(prevalence,thresholdM,thresholdF) {return prevalence >= thresholdF || prevalence <= thresholdM},
fem : function(prevalence,thresholdM,thresholdF) {return prevalence >= thresholdF} // all women
}
// Select relevant meaning function
var meaning = function(utterance, prevalence, thresholdM,thresholdF) {
var uttfn = uttFns[utterance]
return uttfn(prevalence,thresholdM,thresholdF)
}
// Prior model
// Modified from Ch. 7 Generics for stable distribution only
var priorModel = function(params){
Infer({model: function(){
var g = params['prevalenceWhenPresent']
var d = params['concentrationWhenPresent']
var StableDistribution = DiscreteBeta(g, d)
return sample(StableDistribution)
}})
}
// Prevalence when present for representative professions
var professions = {camio: {prevalence: .21}, // truck driver
medic: {prevalence: .51}, // doctor
peluq: {prevalence: .79}} // hairdresser
// Get profession from lookup table
var prof_lookup = function(job){
return professions[job]
}
// Query a profession and get the prevalence when present
var prof = 'peluq'
var prof_params = prof_lookup(prof)
// Define prior for a profession
var prior = priorModel({
prevalenceWhenPresent: prof_params.prevalence,
concentrationWhenPresent: 20
})
// Literal listener (L0)
// cf. Ch. 7 Generic Language
var listener = function(utterance, statePrior,thresholdM,thresholdF) {
Infer({model: function(){
var prevalence = uniformDraw(bins)
var m = meaning(utterance, prevalence, thresholdM,thresholdF)
condition(m)
return prevalence
}})
}
var alpha = 4;
// Speaker (S)
// Modified from Ch. 7 Generics to weight cost by stereotype strength
var speaker = function(prevalence, statePrior,thresholdM,thresholdF){
// get strength of stereotype
var strength = Math.abs(prevalence - 0.5)
Infer({model: function(){
var utterance = utterancePrior();
var L = listener(utterance, statePrior, thresholdM,thresholdF);
// factor( alpha * (L.score(prevalence) - cost[utterance] ))
factor( alpha * (L.score(prevalence) - (cost[utterance] * strength) ) )
return utterance
}})
}
// Pragmatic listener (L1)
// Modified from Ch. 5 Vagueness
var pragmaticListener = function(utterance,prior) {
// run inference
return Infer({method: 'enumerate'},
function() {
var prevalence = sample(prior)
var thresholdM = thresholdPriorM()
// var thresholdF = thresholdPriorF()
var thresholdF = thresholdPriorM()
factor( speaker(prevalence, prior,thresholdM,thresholdF).score(utterance) )
return { prevalence: prevalence ,thresholdM: thresholdM, thresholdF: thresholdF}
})
}
// Define func to run model for mslashf, and mascpl utterances
var runsim = function(prior){
map(function(utt){
var L1 = pragmaticListener(utt,prior)
var expect = expectation(marginalize(L1,'prevalence'))
display('expected % women (' + utt + '): ' + expect)
viz(marginalize(L1,'prevalence'))
return expect
}, ['mascpl','mslashf']) // ,'fem'
}
// Run model across the three professions
map(function(prof){
var prof_prev = prof_lookup(prof).prevalence
display(prof + '(prior mean: ' + prof_prev + ')')
var prior = priorModel({
prevalenceWhenPresent: prof_prev,
concentrationWhenPresent: 20
})
runsim(prior)
},['camio','medic','peluq'])
true
For a stereotypically male profession (truck driver; prior mean = 0.21), the model estimates a higher prevalence of women under the high-cost utterance (~39%) relative to the low-cost “default” one (~20%). For a stereotypically neutral profession (doctor; prior mean = 0.51), the model estimates a marginally higher prevalence of women under the high-cost utterance (~51%) than the low-cost one (~47%). Finally, for a stereotypically female profession (hairdresser; prior mean = 0.79), the model estimates a lower prevalence of women under the high-cost utterance (~67%) compared to the low-cost one (~74%).
Contrary to the claims of the RAE, the “default” low-cost masculine plural utterance does not provide uniform expectations over gender distribution regardless of profession, a pattern we have been able to encode here. In the same vein, the behavioral data show that the higher-cost utterance does not necessarily mean “more women” than the low-cost utterance, but can also be used to indicate more men, again a behavior we have been able to mimic with our RSA model. We therefore posit that the high-cost utterance is not used to indicate “more women” but rather to contrast with the listener’s prior expectations about the gender prevalence of the profession.
We find that the model produces a qualitatively human-like pattern with regard to its estimate of the prevalence of women in the professions given the selected utterances. Under the high cost utterance, the model draws posterior mass away from the extrema relative to the lower-cost utterance – the pattern we observe in the human respondents.
In order to achieve these effects, we have specifically innovated in two ways: semantics of the mslashf utterance, and the use of cost-weighting. While the mascpl and fem utterances have straightforward interpretations as meeting some required lower or upper threshold of women respectively, the mslashf utterance is not quite so obvious. By operationalizing the semantics of this utterance as the disjunction of the other two non-null utterances, we appear to have appropriately captured human behavior.
In class, the question was raised as to whether the cost weighting was necessary to produce the observed behavioral results. We found that without the cost weighting, the model always predicted a greater prevalence of women under the mslashf utterance relative to the mascpl one (this can be observed by commenting out the factor statement in the speaker and uncommenting the line above). In essence, the mslashf utterance was serving as an intermediate point between the mascpl (lower prevalence of women) and fem (higher prevalence of women) utterances. It is unclear whether the mechanism we have implemented here is cognitively plausible, but it functions as needed for now.
In a previous version of the model which was presented in class, we used a higher prior for thresholdF; however, this does not appear to be necessary to produce the observed results (but sometimes makes the differences larger).
In short, we have a functioning model to capture an interesting pattern of human linguistic behavior. More work is needed, however, to work out some of the specifics and fit it more accurately to human behavior. One element of this would be a behavioral study which asked participants how many out of a set number (e.g.: 5) of professionals are women given the utterances. In this task we would also need to include a fem utterance in order to round out the priors of the model. This task would help provide a more direct mapping from human behavior to model predictions.
On the modeling side, we hope to implement a pragmatic speaker which will select appropriate utterances for {profession, prevalence} pairs to match up with the pragmatic listener. An initial attempt was made at implementing this speaker but it did not immediately produce the desired effects so it was scrapped for the sake of time.
In addition, we hope to further explore the parameter space for thresholdM and thresholdF to understand how they impact model predictions and interact with one another. We also hope to include an even higher-cost utterance of the form peluqueras o peluqueros which even more explicitly encodes the disjunction implemented in the semantics of the mslashf utterance here.