A social science trust taxonomy with emergent vectors and symmetry

Abstract

Introduction: Trust is foundational to all social science domains, but to date, there is no unifying theory or consistent measurement basis spanning the social sciences. This research hypothesized that trust forms the basis of an ontology that could unify the social science domains. The proposed ontology comprises a Cartesian plane with axes self-trust and other-trust. Self-trust manifests in dominant behaviors, and other-trust manifests in cooperative behaviors. Both axes are divided into five discrete categories, creating a matrix of 25 cells. All words in the lexicon are allocated into one of these 25 cells.

Methods: This research started with an existing 14,000-word lexicon of dominance and affiliation. The lexicon was extended by manually identifying and including socially descriptive words with information regarding self-trust, other-trust, dominance, and cooperation. The taxonomy was optimized using the Gradient Descent machine learning algorithm and commercially curated synonyms and antonyms. The t-test was employed as the objective (or loss) function for Gradient Descent optimization. Word vectors were identified using groups of four words related as synonyms and antonyms.

Results: Over 30,000 words were identified and included in the lexicon. The optimization process yielded a t-score of over 1,000. Over 226,000 vectors were identified, such as malevolent-mean-gentle-benevolent. A new form of symmetry was identified between adjectives and verbs with a common root; for example, the words reject and rejected are horizontally reflected.

Discussion: The word vectors can create a metrologically compliant basis for psychometric testing. The symmetries provide insight into causes (verbs) and effects (adjectives) in social interactions. These vectors and symmetries offer the social sciences a basis of commonality with natural sciences, enabling unprecedented accuracy and precision in social science measurement.

Keywords: cooperation; dimensional models; dominance; lexical analysis; metrology; symmetry; trust; vectors.

Figure 1

Symmetric word vectors. Word vectors are defined as four words on a line starting and ending at the outer edges of the trust ontology and passing through the origin. The outer- and inner pairs of words are associated with each other as antonyms. The left and right pairs are associated with each other as synonyms. The distance between the synonyms can be calculated using the Pythagorean theorem. For example, when the vector lies on the horizontal axis (y = 0), the distance between synonyms is 1, and the distance between antonyms is 4 for the outer pair of antonyms and 2 for the inner pair.

Figure 2

Cardinal vectors spanning the trust taxonomy. The Cartesian coordinates of points along each vector are shown. The Cartesian coordinates also form a 5×5 matrix with 25 cells.

Figure 3

Taxonomy optimization. In this example, the location of three words, ferocious, temperate, and gentle, are shown on the Cartesian plane. ΔST is the difference in self-trust scores, and ΔOT is the difference in other-trust scores. The Pythagorean theorem is used to calculate the distance between synonyms and antonyms, in this instance, 1.41 and 5.66, respectively (see Equations 2, 3). An ideal taxonomy has similar phenomena that are tightly clustered and dissimilar phenomena that are widely separated. The taxonomy optimization process seeks to arrange the words on the Cartesian plane so that the average distance between antonyms is maximized and, concurrently, the average distance between synonyms is minimized.

Figure 4

Synonym and antonym density plots. Density plots visually represent the location of synonyms and antonyms on the Cartesian plane. (A–H) Example density plots for 16 words located in the outer layer of the taxonomy. (I–L) Horizontal symmetry of verbs and adjectives with the suffix ed. (M–Y) Synonym density plots with words pertinent to the social sciences, law, economics, education, and psychology.

Figure 5

Example vectors spanning the taxonomy. (A) Noun (B) Adjectives (C) Verbs (D) Gerunds (E) Abstract Nouns (F) Adverbs. These vectors are consonant combinations of words related as synonyms and antonyms, created using the process as shown in Figure 2. (A) No noun vectors were identified for two of the eight cardinal vectors, denoted by n/a. Nouns generally had fewer synonyms than other parts of speech, and therefore, fewer noun vectors were identified compared to other parts of speech.