Interaction of two walkers: wave-mediated energy and force.

A bouncing droplet, self-propelled by its interaction with the waves it generates, forms a classical wave-particle association called a "walker." Previous works have demonstrated that the dynamics of a single walker is driven by its global surface wave field that retains information on its past trajectory. Here we investigate the energy stored in this wave field for two coupled walkers and how it conveys an interaction between them. For this purpose, we characterize experimentally the "promenade modes" where two walkers are bound and propagate together. Their possible binding distances take discrete values, and the velocity of the pair depends on their mutual binding. The mean parallel motion can be either rectilinear or oscillating. The experimental results are recovered analytically with a simple theoretical framework. A relation between the kinetic energy of the droplets and the total energy of the standing waves is established.

Universal size effects for populations in group-outcome decision-making problems.

Elections constitute a paradigm of decision-making problems that have puzzled experts of different disciplines for decades. We study two decision-making problems, where groups make decisions that impact only themselves as a group. In both studied cases, participation in local elections and the number of democratic representatives at different scales (from local to national), we observe a universal scaling with the constituency size. These results may be interpreted as constituencies having a hierarchical structure, where each group of N agents, at each level of the hierarchy, is divided in about N(δ) subgroups with δ≈1/3. Following this interpretation, we propose a phenomenological model of vote participation where abstention is related to the perceived link of an agent to the rest of the constituency and which reproduces quantitatively the observed data.

Between order and disorder: a 'weak law' on recent electoral behavior among urban voters?

A new viewpoint on electoral involvement is proposed from the study of the statistics of the proportions of abstentionists, blank and null, and votes according to list of choices, in a large number of national elections in different countries. Considering 11 countries without compulsory voting (Austria, Canada, Czech Republic, France, Germany, Italy, Mexico, Poland, Romania, Spain, and Switzerland), a stylized fact emerges for the most populated cities when one computes the entropy associated to the three ratios, which we call the entropy of civic involvement of the electorate. The distribution of this entropy (over all elections and countries) appears to be sharply peaked near a common value. This almost common value is typically shared since the 1970s by electorates of the most populated municipalities, and this despite the wide disparities between voting systems and types of elections. Performing different statistical analyses, we notably show that this stylized fact reveals particular correlations between the blank/null votes and abstentionists ratios. We suggest that the existence of this hidden regularity, which we propose to coin as a 'weak law on recent electoral behavior among urban voters', reveals an emerging collective behavioral norm characteristic of urban citizen voting behavior in modern democracies. Analyzing exceptions to the rule provides insights into the conditions under which this normative behavior can be expected to occur.

Election turnout statistics in many countries: similarities, differences, and a diffusive field model for decision-making.

We study in details the turnout rate statistics for 77 elections in 11 different countries. We show that the empirical results established in a previous paper for French elections appear to hold much more generally. We find in particular that the spatial correlation of turnout rates decay logarithmically with distance in all cases. This result is quantitatively reproduced by a decision model that assumes that each voter makes his mind as a result of three influence terms: one totally idiosyncratic component, one city-specific term with short-ranged fluctuations in space, and one long-ranged correlated field which propagates diffusively in space. A detailed analysis reveals several interesting features: for example, different countries have different degrees of local heterogeneities and seem to be characterized by a different propensity for individuals to conform to the cultural norm. We furthermore find clear signs of herding (i.e., strongly correlated decisions at the individual level) in some countries, but not in others.

Emergence of time-horizon invariant correlation structure in financial returns by subtraction of the market mode.

We investigate the emergence of a structure in the correlation matrix of assets' returns as the time horizon over which returns are computed increases from the minutes to the daily scale. We analyze data from different stock markets (New York, Paris, London, Milano) and with different methods. In addition to the usual correlations, we also analyze those obtained by subtracting the dynamics of the "center of mass" (i.e., the market mode). We find that when the center of mass is not removed the structure emerges, as the time horizon increases, from splitting a single large cluster into smaller ones. By contrast, when the market mode is removed the structure of correlations observed at the daily scale is already well defined at very high frequency (5 min in the New York Stock Exchange). Moreover, this structure accounts for 80% of the classification of stocks in economic sectors. Similar results, though less sharp, are found for the other markets. We also find that the structure of correlations in the overnight returns is markedly different from that of intraday activity.

Chaotic, staggered, and polarized dynamics in opinion forming: The contrarian effect.

We reconsider the no-tie-breaking two-state Galam contrarian model of opinion dynamics for update groups of size 3. While the initial model assumes a constant density of contrarians a for both opinions, the density now depends for each opinion on its global support. Proportionate contrarians are thus found to indeed preserve the main results of the former case. However, restricting the contrarian behavior to only the current collective majority makes the dynamics more complex with additional features. For a density a < a(c) = 1/9 of one-sided contrarians, a chaotic basin is found in the 50-50 region separated from two majority-minority point attractors, one on each side. For 1/9 < a less similar to 0.301 only the chaotic basin survives. In the range a > 0.301 the chaotic basin disappears and the majority starts to alternate between the two opinions with a staggered flow toward two point attractors. We then study the effect of both decoupling the local update time sequence from the contrarian behavior activation and a smoothing of the majority rule. A status quo-driven bias for contrarian activation is also considered. Introduction of unsettled agents driven in the debate on a contrarian basis is shown only to shrink the chaotic basin. The model may shed light on recent apparent contradictory elections with on the one hand very close results as in the United States in 2000 and in Germany in 2002 and 2005, and on the other hand, a huge majority as in France in 2002.