Analysis of the distribution of the number of bidders in construction contract auctions

The number of bidders, N, involved in a construction procurement auction is known to have an important effect on the value of the lowest bid and the mark-up applied by bidders. In practice, for example, it is important for a bidder to have a good estimate of N when bidding for a current contract. One approach, instigated by Friedman in 1956, is to make such an estimate by statistical analysis and modelling. Since then, however, finding a suitable model for N has been an enduring problem for researchers and, despite intensive research activity in the subsequent 30 years, little progress has been made, due principally to the absence of new ideas and perspectives. The debate is resumed by checking old assumptions, providing new evidence relating to concomitant variables and proposing a new model. In doing this and in order to ensure universality, a novel approach is developed and tested by using a unique set of 12 construction tender databases from four continents. This shows the new model provides a significant advancement on previous versions. Several new research questions are also posed and other approaches identified for future study.

Tests of sunspot number sequences: 1. Using ionosonde data

More than 70 years ago it was recognised that ionospheric F2-layer critical frequencies [foF2] had a strong relationship to sunspot number. Using historic datasets from the Slough and Washington ionosondes, we evaluate the best statistical fits of foF2 to sunspot numbers (at each Universal Time [UT] separately) in order to search for drifts and abrupt changes in the fit residuals over Solar Cycles 17-21. This test is carried out for the original composite of the Wolf/Zürich/International sunspot number [R], the new “backbone” group sunspot number [RBB] and the proposed “corrected sunspot number” [RC]. Polynomial fits are made both with and without allowance for the white-light facular area, which has been reported as being associated with cycle-to-cycle changes in the sunspot number - foF2 relationship. Over the interval studied here, R, RBB, and RC largely differ in their allowance for the “Waldmeier discontinuity” around 1945 (the correction factor for which for R, RBB and RC is, respectively, zero, effectively over 20 %, and explicitly 11.6 %). It is shown that for Solar Cycles 18-21, all three sunspot data sequences perform well, but that the fit residuals are lowest and most uniform for RBB. We here use foF2 for those UTs for which R, RBB, and RC all give correlations exceeding 0.99 for intervals both before and after the Waldmeier discontinuity. The error introduced by the Waldmeier discontinuity causes R to underestimate the fitted values based on the foF2 data for 1932-1945 but RBB overestimates them by almost the same factor, implying that the correction for the Waldmeier discontinuity inherent in RBB is too large by a factor of two. Fit residuals are smallest and most uniform for RC and the ionospheric data support the optimum discontinuity multiplicative correction factor derived from the independent Royal Greenwich Observatory (RGO) sunspot group data for the same interval.