SOWA: Spatial Ordered Weighted Averaging

Strengths

• •Explicitly models spatially heterogeneous risk attitudes through zone-specific ORness
• •Inherits OWA's full ORness-trade-off flexibility within each zone
• •Reduces to standard OWA (one zone) or WLC (uniform λ=1/n): no discontinuity
• •Counterfactual scores (what-if zone reassignment) are computationally trivial and illustrative

Limitations

• •Zone_order_weights are difficult to elicit: requires domain expert knowledge of spatial risk attitudes
• •Results are sensitive to zone boundary definition
• •Alternatives with extreme criterion profiles (high best, low worst) are most affected by zone ORness: this can appear counter-intuitive
• •Spatial heterogeneity of risk attitudes may be better modelled continuously (e.g. distance-decay ORness) rather than discretely

Assumptions to verify

• •Zone boundaries are meaningful and justified (e.g. hazard zones, administrative districts)
• •Each zone's λ vector correctly encodes the spatial risk attitude of that region
• •Criterion weights w_k are globally applicable (same importance across all zones)
• •Value-scaling to [0,1] is appropriate before aggregation

When not to use

• •Non-spatial problem: alternatives have no zone assignment → use OWA
• •All zones have identical risk attitude → standard OWA is simpler
• •Zone order-weights cannot be elicited from domain knowledge → spatial extension is arbitrary

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