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Opinion and consensus dynamics in tourism digital ecosystems

Rodolfo BaggioBocconi University, Italy

Giacomo Del ChiappaUniversity of Sassari and CRENoS, Italy

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Background (1)

The Web is not simply a technological manifestation but a reflection of social structures and processes

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Background (2)

Tourism destination : digital business ecosystem– dynamically interlinked real and virtual agents – digital components are intelligent, active and adaptive

organisms– system is in continuous evolution (perpetual beta)

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Tourism digital ecosystem

Effici

ency

System structure affects functions

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Background (3)

• Collaboration, harmonization and coordination of stakeholders’ views pivotal for effective & competitive tourism development

• Enforced through consensus building

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Objectives

• Reconfirm, on more solid bases, structural interdependence of real & virtual components in a tourism digital ecosystem

• Investigate how digital ecosystem topology affects opinion sharing & consensus development among stakeholders

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Materials• Three Italian destinations

– Elba, Gallura, Livigno– Similar size ( 1000 firms)– Similar tourism intensity

(500k tourists/year, strong seasonality)

• Collected data & built network– core tourism operators +

websites– links btw firms & websites

• also weighted

Livigno

Elba

Gallura

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Materials

Cum

ulati

ve d

eg. d

istr

ib.

Similar characteristics& topology

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Dynamic processes

• Information diffusion– epidemiological models on network substrate; – main parameter: infectivity τ – infection process possible when τ > τC (critical threshold)

• Synchronization– models consensus formation– physical model by Kuramoto: system elements are coupled

oscillators, each with intrinsic frequency & characteristic phase– main parameter: coupling K – whole system synchronises when K > KC (critical coupling)

(i.e. all oscillators have same phase -> opinions are aligned)• NB: critical values depend on system configuration

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Nets, matrices, eigenvalues & eigenvectors

• For a square (nn) matrix M, it is possible to find a scalar λ and a vector xn10 satisfying Mx = λx.

• λ, x are called eigenvalues & eigenvectors of M; – a real symmetric nn matrix M has n real eigenvalues– the set of distinct eigenvalues is called the spectrum of M

• Eigenvalues and eigenvectors “summarize” network topology– eigenvalues: global information,

eigenvectors: local (nodal) information

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Methods

• Spectral analysis, i.e. analysis of the eigenvalues and eigenvector of the adjacency & Laplacian matrices of the 3 networks– useful, and often computationally more efficient, way to

assess network main parameters

Adjacency matrix:

Laplacian matrix:

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Methods

Use 2 results from graph spectral theory:• Fiedler vector: eigenvector associated with second

smallest Laplacian eigenvalue 2 renders algebraic connectivity of the network– large gaps in plot separation between “communities”

• Spectral radius: largest eigenvalue of adjacency matrix λN

– SIS epidemic diffusion in undirected graph: critical threshold τC = 1/λN

– Synchronization: critical coupling KC 1/λN

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Results: topologyFiedler vector

Artificial network w. 2well separated modules

No trivial separation possible

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Results: diffusion & synchronization

• The values for whole ecosystems < those of single components (minimum is for weighted networks)

NB: weights assigned to links considering probable cost of links (RR=1, VR=2, VV=3)

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Concluding remarks

• Reconfirm that no trivial structural separation is possible between real and virtual components in a tourism system

• Combination of real and virtual elements in a single integrated system provides a more efficient substrate for the spreading of ideas or the reaching of a consensus on some issue