37 research outputs found
Analysing the Notion of 'Consumer' in China’s Consumer Protection Law
The notion of ‘consumer’ in Article 2 of the People’s Republic of China (PRC)’s Consumer Protection Law has been subject to criticism as it is vague, can be difficult to apply to real life situations, and is also at odds with the notion of a ‘consumer’ found in other jurisdictions around the world. This article will discuss the Chinese legislative definition of a ‘consumer’ from a comparative perspective before considering how this notion has been applied by the courts, by analysing several Guiding Cases issued by China’s Supreme People’s Court (SPC) and judgments in which the Guiding Cases have been subsequently applied. The article will then consider the delicate balance that the courts in China are attempting to strike between encouraging consumer claimants to pursue fraudulent traders and yet discouraging consumers from exploiting the punitive damages provisions of the PRC Consumer Protection Law. Thus, this detailed analysis of the legal notion of a ‘consumer’ in China offers a unique and powerful insight into the wider role of consumers within the Chinese legal system
Consistent distribution-free -sample and independence tests for univariate random variables
A popular approach for testing if two univariate random variables are
statistically independent consists of partitioning the sample space into bins,
and evaluating a test statistic on the binned data. The partition size matters,
and the optimal partition size is data dependent. While for detecting simple
relationships coarse partitions may be best, for detecting complex
relationships a great gain in power can be achieved by considering finer
partitions. We suggest novel consistent distribution-free tests that are based
on summation or maximization aggregation of scores over all partitions of a
fixed size. We show that our test statistics based on summation can serve as
good estimators of the mutual information. Moreover, we suggest regularized
tests that aggregate over all partition sizes, and prove those are consistent
too. We provide polynomial-time algorithms, which are critical for computing
the suggested test statistics efficiently. We show that the power of the
regularized tests is excellent compared to existing tests, and almost as
powerful as the tests based on the optimal (yet unknown in practice) partition
size, in simulations as well as on a real data example.Comment: arXiv admin note: substantial text overlap with arXiv:1308.155
Eigenstripping, Spectral Decay, and Edge-Expansion on Posets
Fast mixing of random walks on hypergraphs (simplicial complexes) has recently led to myriad breakthroughs throughout theoretical computer science. Many important applications, however, (e.g. to LTCs, 2-2 games) rely on a more general class of underlying structures called posets, and crucially take advantage of non-simplicial structure. These works make it clear that the global expansion properties of posets depend strongly on their underlying architecture (e.g. simplicial, cubical, linear algebraic), but the overall phenomenon remains poorly understood. In this work, we quantify the advantage of different poset architectures in both a spectral and combinatorial sense, highlighting how regularity controls the spectral decay and edge-expansion of corresponding random walks.
We show that the spectra of walks on expanding posets (Dikstein, Dinur, Filmus, Harsha APPROX-RANDOM 2018) concentrate in strips around a small number of approximate eigenvalues controlled by the regularity of the underlying poset. This gives a simple condition to identify poset architectures (e.g. the Grassmann) that exhibit strong (even exponential) decay of eigenvalues, versus architectures like hypergraphs whose eigenvalues decay linearly - a crucial distinction in applications to hardness of approximation and agreement testing such as the recent proof of the 2-2 Games Conjecture (Khot, Minzer, Safra FOCS 2018). We show these results lead to a tight characterization of edge-expansion on expanding posets in the ??-regime (generalizing recent work of Bafna, Hopkins, Kaufman, and Lovett (SODA 2022)), and pay special attention to the case of the Grassmann where we show our results are tight for a natural set of sparsifications of the Grassmann graphs. We note for clarity that our results do not recover the characterization of expansion used in the proof of the 2-2 Games Conjecture which relies on ?_? rather than ??-structure